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BEGIN:VEVENT
SUMMARY:Jeroen Lamb (Imperial College London)
DTSTART:20201123T150000Z
DTEND:20201123T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/1
DESCRIPTION:Title: Bifurcation in the presence of noise\nby Jeroen Lamb (Imp
erial College London) as part of UAB dynamical systems group international
seminar\n\n\nAbstract\nWe discuss some recent progress in the development
of a\nbifurcation theory for random dynamical systems\, touching upon\nth
e following publications:\n\n- Maximilian Engel\, Jeroen S. W. Lamb\, and
Martin Rasmussen\, Bifurcation\nanalysis of a stochastically driven limit
cycle\, Communications in\nMathematical Physics 365\, 3 (2019)\, 935−942
.\n\n- Maximilian Engel\, Jeroen S. W. Lamb\, and Martin Rasmussen\, Condi
tioned\nLyapunov exponents for random dynamical systems\, Transactions of
the\nAmerican Mathematical Society 372\, 9 (2019)\, 6343−6370.\n\n- Thai
Son Doan\, Maximilian Engel\, Jeroen S. W. Lamb\, and Martin\nRasmussen\,
Hopf bifurcation with additive noise\, Nonlinearity 31\, 10\n(2018)\, 456
7−4601.\n\n- Mark Callaway\, Thai Son Doan\, Jeroen S. W. Lamb\, and Mar
tin Rasmussen\,\nThe dichotomy spectrum for random dynamical systems and p
itchfork\nbifurcations with additive noise\, Annales de l'Institut Henri P
oincaré\nProbabilités et Statistiques 53\, 4 (2017)\, 1548−1574.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Villari (Università degli Studi di Firenze)
DTSTART:20201130T150000Z
DTEND:20201130T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/2
DESCRIPTION:Title: Recent contributions and some open questions in the qualitati
ve behaviour of certain generalized Liénard equations\nby Gabriele Vi
llari (Università degli Studi di Firenze) as part of UAB dynamical system
s group international seminar\n\n\nAbstract\nThe aim of this talk is to pr
esent some recent results\, together with some\nopen questions\, concernin
g the phase-portrait of certain generalized Liénard\nequations.\nAt frst
I will briefly discuss some joint work with Jean Mawhin\, Fabio Zanolin an
d Timoteo Carletti for the relativistic Liénard equation\n$$\n\\frac{d}{d
x}\\frac{\\dot{x}}{\\sqrt{1-x^2}}+f(x)\\dot{x}+g(x)=0\n$$\nas well as for
the case with prescrived curvature\n$$\n\\frac{d}{dx}\\frac{\\dot{x}}{\\sq
rt{1-x^2}}+\\lambda{}f(x)\\dot{x}+g(x)=0\n$$\nIn this framework\, a genera
lization in wich a function $f (x\,\\dot{x})$ takes the role\nof the funct
ion $f (x)$ will be also presented.\nHowever\, the main part of the talk w
ill concentrate on a very recent joint\nresult with Fabio Zanolin\, concer
ning the generalized Liénard system\n$$\n\\dot{x} = y − F (x\, y)\\\\\n
\\dot{y} = −g(x)\n$$\nand focusing on the case in which\n$F (x\, y) = \\
lambda{}B(y)A(x)$\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josep Maria Cors (Universitat Politècnica de Catalunya)
DTSTART:20201214T150000Z
DTEND:20201214T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/3
DESCRIPTION:Title: A tour around Central Configurations\nby Josep Maria Cors
(Universitat Politècnica de Catalunya) as part of UAB dynamical systems
group international seminar\n\n\nAbstract\nIn Celestial Mechanics a config
uration of the $N$-body problem is\ncentral if the acceleration vector for
each body is a common scalar\nmultiple of its position vector (with respe
ct to the center of mass).\nThe aim of the talk is to visit some of the re
cently studied problems:\n$1+n$\, Co-circular\, Crowns\, Stacked five body
-problem\, Convex four\nbody-problem\, ... to get the feeling of the topic
.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Peralta-Salas (Instituto de Ciencias Matemáticas)
DTSTART:20201221T150000Z
DTEND:20201221T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/4
DESCRIPTION:Title: New results on the dynamics of the steady Euler flows\nby
Daniel Peralta-Salas (Instituto de Ciencias Matemáticas) as part of UAB
dynamical systems group international seminar\n\n\nAbstract\nA volume-pres
erving vector field $X$ on a manifold $M$ is Eulerisable if there exists a
Riemannian metric $g$ on $M$ such that $X$ satisfies the stationary Euler
equations on $(M\,g)$. In this talk I will review some recent results on
the dynamics of Eulerisable flows. In the first part I will present a homo
logical characterization which generalizes the classical one by Sullivan f
or geodesible flows\; as an application\, I will show that this result imp
lies that the Eulerisable flows cannot exhibit (volume-preserving) plugs.
This is based on joint work with Ana Rechtman and Francisco Torres de Liza
ur. In the second part\, I will show that the Eulerisable flows are univer
sal in the sense of Tao\, i.e.\, any non-autonomous dynamics is extendable
to an Euler flow on a sphere of sufficiently high dimension for some Riem
annian metric. This implies\, in particular\, the Turing completeness of t
he Euler fields. This is based on joint work with Robert Cardona\, Eva Mir
anda and Francisco Presas.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Rademacher (Universität Bremen)
DTSTART:20210111T150000Z
DTEND:20210111T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/5
DESCRIPTION:Title: Pulse replication and accumulation of eigenvalues\nby Jen
s Rademacher (Universität Bremen) as part of UAB dynamical systems group
international seminar\n\n\nAbstract\nThis talk concerns the spatial dynami
cs approach to dynamical phenomena in partial differential equations (PDE)
posed on the real line. Motivated by pulse-replication phenomena observed
in the FitzHugh--Nagumo equation\, traveling pulses whose slow-fast profi
les exhibit canard-like transitions are investigated. It is shown that the
spectra of the PDE linearization about such pulses may contain many point
eigenvalues that accumulate onto a union of curves as the slow scale para
meter approaches zero. The limit sets are related to the absolute spectrum
of the homogeneous rest states involved in the canard-like transitions.\n
This is joint work with Paul Carter (Minneapolis) and Bjorn Sandstede (Pro
vidence)\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Panazzolo (Université de Haute-Alsace)
DTSTART:20210118T150000Z
DTEND:20210118T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/6
DESCRIPTION:Title: Versal regularization of vector fields with cross type discon
tinuities.\nby Daniel Panazzolo (Université de Haute-Alsace) as part
of UAB dynamical systems group international seminar\n\n\nAbstract\nI will
expose some aspects of the regularization of vector fields with discontin
uities along non-smooth sets. The basic problem in the background is to de
velop a theory of versal regularisations\, which captures all possible dy
namics resulting from changing the regularization method.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tere M. Seara (Universitat Politècnica de Catalunya)
DTSTART:20210125T150000Z
DTEND:20210125T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/7
DESCRIPTION:Title: Non existence of small amplitude breathers for the reversible
Klein-Gordon equation\nby Tere M. Seara (Universitat Politècnica de
Catalunya) as part of UAB dynamical systems group international seminar\n\
n\nAbstract\nBreathers are periodic in time spatially localized solutions
of evolutionary PDEs. They are known to exist for the sine-Gordon equation
but are believed to be rare in other Klein-Gordon equations. Exchanging t
he roles of time and position\, breathers can be interpreted as homoclinic
solutions to a steady solution.\n\nIn this talk\, I will explain how to s
how that\, under generic asumptions\, the Klein-Gordon equation does not h
ave breathers whose amplitude is smaller than a certain quantity. The key
point is to obtain an asymptotic formula for the distance between the stab
le and unstable manifold of the steady solution when the steady solution h
as weakly hyperbolic one dimensional stable and unstable manifolds. Their
distance is exponentially small with respect to the amplitude of the breat
her and therefore classical perturbative techniques cannot be applied.\n\n
This is a joint work with O. Gomide (Universidade Federal de Goiás)\, M.
Guardia (U. Politecnica de Catalunya) and C. Zeng (Georgiatech I.)\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Douglas Duarte Novaes (Universidade Estadual de Campinas)
DTSTART:20210201T150000Z
DTEND:20210201T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/8
DESCRIPTION:Title: Sliding Shilnikov dynamics in non-smooth systems and applicat
ions.\nby Douglas Duarte Novaes (Universidade Estadual de Campinas) as
part of UAB dynamical systems group international seminar\n\n\nAbstract\n
In the theory of piecewise smooth vector fields a Sliding Shilnikov Orbit
is a trajectory\, in the\nFilippov sense\, connecting a saddle focus pseud
o-equilibrium to itself. Recently\, it has been shown\nthat this connectio
n provides a chaotic dynamic without further assumptions. \nIn this talk\,
we explore the dynamics of this connection and an application for biologi
cal models is presented.\n\n\nReferences:\n\nD.D. Novaes\, G. Ponce\, and
R. Varão\, Chaos induced by sliding phenomena in Filippov systems\, J. Dy
n. Diff. Equat. 29 (2017)\, 1569-1583.\n\nD.D.Novaes and M. A. Teixeira\,
Shilnikov problem in nonsmooth dynamical systems\, Chaos 29\, 063110 (2019
).\n\nT. Carvalho\, D.D. Novaes\, and L.F. Gonçalves\, Sliding Shilnikov
Connection in Filippov-type Predator-Prey Model\, Nonlinear Dynamics\, 100
(3)\, 2973-2987.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chara Pantazi (Universitat Politècnica de Catalunya)
DTSTART:20210208T150000Z
DTEND:20210208T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/9
DESCRIPTION:Title: Integrability and linearizability for some families of three
dimensional quadratic systems\nby Chara Pantazi (Universitat Politècn
ica de Catalunya) as part of UAB dynamical systems group international sem
inar\n\n\nAbstract\nThis talk concerns the problem of local integrability
at the origin of some families in three dimensions. First I present some r
esults about the local integrability at the origin of a nine parametric fa
mily of a three dimensional Lotka--Volterra differential systems with 3:-1
:2-resonance. More concrete I present the necessary and sufficient conditi
ons on the parameters of the family that guarantee the existence of two i
ndependent local first integrals at the origin of coordinates. Additionall
y\, I present the cases where the origin is linearizable. Then\, I presen
t a study of another nine parametric family of quadratic systems with 1:-
2:1 resonance at the origin and the axes planes do not need to be invaria
nt. For some subfamily I present the conditions that guarantee the non-exi
stence of a polynomial first integral.\n\nThe first part of the talk is a
joint work with W. Aziz(Salahaddin University-Erbil\, Iraq)\, C. Christoph
er(Plymouth University\, UK) and J. Llibre(UAB\, Catalonia\,Spain). The se
cond part of the talk is a joint work with W. Aziz(Salahaddin University-E
rbil\, Iraq) and A. Amen(Salahaddin University-Erbil\, Iraq).\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Luis Bravo (Universidad de Extremadura)
DTSTART:20210222T150000Z
DTEND:20210222T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/10
DESCRIPTION:Title: Generating non-trivial limit cycles in Abel equations\nb
y José Luis Bravo (Universidad de Extremadura) as part of UAB dynamical s
ystems group international seminar\n\n\nAbstract\nLet us fix trigonometric
monomials $A_k$ and integers $n_k\\geq 1$\, $k=1\,\\ldots\,m$\, and\ncons
ider the family of Abel-like differential equations\n$$x'=\\sum_{k=1}^m a_
k A_k(t) x^{n_k}\,$$ where $a_k\\in\\mathbb{R}$.\n\nThis equation always h
as the trivial solution $x(t)\\equiv 0$. Moreover\,\neither every bounded
solution is $2\\pi$-periodic or $2\\pi$-periodic solutions\nare isolated.
In the first case\, we say that the equation has a center\nand in the seco
nd case\, we call limit cycle to any $2\\pi$-periodic solution.\n\nWe are
interested in studying whether there exist equations\nof the family with n
on-trivial limit cycles. That is\, if there exist $a_1\,\\ldots\,a_m$\nsuc
h that the differential equation has a limit cycle different from $x(t)=0$
.\n\nWe will focus on the special case $\\{n_k\\colon k=1\,\\ldots m\\}=\\
{n_1\,n_2\\}$\, $n_1\,n_2\\geq 2$ and $n_1\\neq n_2$.\nIn this case\, we w
ill ``almost'' determine all the families having equations with non-trivia
l\nlimit cycles. This ``almost'' is due to a special family in which we ha
ve not been able to determine\nwhether there exist or not non-trivial limi
t cycles\, though we suspect the existence of non-trivial limit cycles.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilei Tang (Shanghai Jaio Tong University)
DTSTART:20210301T150000Z
DTEND:20210301T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/11
DESCRIPTION:Title: Some results of limit cycles in Lienard systems and applicat
ions\nby Yilei Tang (Shanghai Jaio Tong University) as part of UAB dyn
amical systems group international seminar\n\n\nAbstract\nThe aim of this
talk is to present our some recent results of limit cycles in planar smoot
h and piecewise smooth Lienard differential systems\, including existence\
, uniqueness\, stability and hyperbolicity of limit cycles.\nMoreover\, us
ing these results for the limit cycles together with other qualitative met
hods and techniques\, we can obtain the exact number of limit cycles and f
urther obtain the global dynamics and bifurcations in some biological and
mechanical models.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Muldowney (University of Alberta)
DTSTART:20210308T150000Z
DTEND:20210308T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/12
DESCRIPTION:Title: Bendixson Conditions for Differential Equations in a Banach
Space\nby James Muldowney (University of Alberta) as part of UAB dynam
ical systems group international seminar\n\n\nAbstract\nA Bendixson Condit
ion precludes the invariance of Jordan curves with respect to the dynamics
of a differential equation $x’ = f(x)$. Thus\, for example\, non-consta
nt periodic orbits and homoclinic cycles are ruled out. As we know\, for 2
-dimensional systems if div f is non-zero in a simply connected open set U
in the plane\, we know that there are no periodic orbits in U. We will ex
plore such conditions in various finite and infinite dimensional spaces.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Walcher (RWTH Aachen)
DTSTART:20210315T150000Z
DTEND:20210315T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/13
DESCRIPTION:Title: Characteristic curves of (quasi-)homogeneous vector fields\nby Sebastian Walcher (RWTH Aachen) as part of UAB dynamical systems gr
oup international seminar\n\n\nAbstract\nCharacteristic curves of homogene
ous vector fields have in recent years experienced a kind of renaissance\,
due to interest in "eigenvectors of tensors" from various applications. I
n the seminar talk we relate the general concept for quasi-homogeneous vec
tor fields to symmetry properties\, and present and extend some existence
results. Moreover an application to finding degree bounds for semi-invaria
nts of polynomial vector fields will be discussed\, as well as an applicat
ion to determining the structure of the centralizer of a local analytic or
formal vector field.\nThe talk reports on recent joint work with G. Gaeta
\, N. Kruff\, J. Llibre\, C. Pantazi and X. Zhang (in various combinations
).\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Martí Pete (University of Liberpool)
DTSTART:20210215T150000Z
DTEND:20210215T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/14
DESCRIPTION:Title: On the computability of Julia sets in the exponential family
\nby David Martí Pete (University of Liberpool) as part of UAB dynami
cal systems group international seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adriana Buică (Universitatea Babeș-Bolyai Cluj-Napoca)
DTSTART:20210322T150000Z
DTEND:20210322T160000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/15
DESCRIPTION:Title: Ulam-Hyers stability and exponentially dichotomic evolution
equations in Banach spaces\nby Adriana Buică (Universitatea Babeș-Bo
lyai Cluj-Napoca) as part of UAB dynamical systems group international sem
inar\n\n\nAbstract\nIn 1941 D. Hyers gave an answer to the following quest
ion of S. Ulam. "Suppose that f satisfies only approximately the equation
$f(x+y)=f(x)+f(y)$. Then does there exist a solution of this equation whic
h f approximates?" Since then\, this type of stability was studied for fun
ctional equations\, difference equations\, and differential equations\, to
o. The first notable result for differential equations is that $x'=\\lambd
a{}x$ is Ulam-Hyers\nstable on $\\mathbb{R}$ if and only if $\\lambda\\neq
0$. In this talk we prove that the system $X'=AX$ is Ulam-Hyers stable on
$\\mathbb{R}$ if and only if $A$ is hyperbolic. We generalize this result
for evolution\nfamilies in Banach spaces using results from the book Evol
ution Semigroups in Dynamical Systems and Differential Equations by C. Chi
cone and Y. Latushkin. The stability is maintained when adding a nonlinear
term which is globally Lipschitz and whose Lipschitz constant is sufficie
ntly small.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Mawhin (Université Catholique de Louvain)
DTSTART:20210426T140000Z
DTEND:20210426T150000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/16
DESCRIPTION:Title: Zeros and surjectivity of continuous mappings in $R^n$\n
by Jean Mawhin (Université Catholique de Louvain) as part of UAB dynamica
l systems group international seminar\n\n\nAbstract\nIn this lecture\, we
use Brouwer degree to obtain in a simple way a number of results on the ex
istence of zeros and the surjectivity of continuous nonlinear mappings in
$n$-dimensional Euclidian space.\n\nThe results generalize and unify a nu
mber of classical ones\, like the Hadamard and the Poincaré-Miranda theor
em\, and some of them make use of possibly discontinuous auxiliary mapping
s and of convexity techniques.\n\nMost of them can be extended to some spe
cial classes of mappings in Banach spaces.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiang Zhang (Shanghai Jiao Tong University)
DTSTART:20210412T140000Z
DTEND:20210412T150000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/17
DESCRIPTION:Title: Jacobian conjecture in $\\mathbb{R}^2$\nby Xiang Zhang (
Shanghai Jiao Tong University) as part of UAB dynamical systems group inte
rnational seminar\n\n\nAbstract\nIn this talk we introduce our solution to
Jacobian conjecture in $\\mathbb{R}^2$. The main tools are from qualitati
ve theory of dynamical systems.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Bonckaert (Hasselt University)
DTSTART:20210503T140000Z
DTEND:20210503T150000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/18
DESCRIPTION:Title: Planar saddle points and formal Gevrey series\nby Patric
k Bonckaert (Hasselt University) as part of UAB dynamical systems group in
ternational seminar\n\n\nAbstract\nPlanar vector fields $X$ near a saddle
type $p:-p$ resonant singular point are considered. The use of Ecalle-Rous
sarie log-like compensators in linearizing conjugacies is carried out\, a
nd Gevrey-type estimates are presented. Attention is given to the unfoldin
g of the resonance with one parameter.\n\nIn the analytic case an approxim
ative normal form with a flat remainder of an explicit type is described\,
including parameter dependence\, also in the (formally linearizable) non-
resonant case.\n\nFinally\, we indicate some questions in the non-resonant
case\, about the possible use of compensators related to the rational app
roximants.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulij S. Ilyashenko (National Research University Higher School of
Economics\, Moscow)
DTSTART:20210531T130000Z
DTEND:20210531T140000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/19
DESCRIPTION:Title: Large bifurcation supports\nby Yulij S. Ilyashenko (Nati
onal Research University Higher School of Economics\, Moscow) as part of U
AB dynamical systems group international seminar\n\n\nAbstract\nGlobal bif
urcation theory on the sphere is now in the study of its creation. The sub
ject of the talk is: given a degenerate vector field\, determine\, what pa
rt of its phase portrait actually bifurcates? The talk is devoted to an an
swer to this question obtained in a joint work with Natalya Goncharuk. Thi
s answer is expected to be a powerful tool in the study of classification
and structural stability of generic families of vector fields on the spher
e with an arbitrary number of parameters.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Liz (Universidade de Vigo)
DTSTART:20210510T140000Z
DTEND:20210510T150000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/20
DESCRIPTION:Title: Four bifurcations and a global stability result in a family
of delay differential equations\nby Eduardo Liz (Universidade de Vigo)
as part of UAB dynamical systems group international seminar\n\n\nAbstrac
t\nIn this lecture\, we introduce a family of delay-differential equations
with many applications in various fields such as economics\, population d
ynamics and physiological systems.\nWe present some new results on the glo
bal dynamics of this equation\, focusing on a particular but representativ
e example. Bifurcation diagrams using relevant model parameters show some
interesting features\, such as stability switches and extinction windows
due to sudden collapses.\nFor the general case\, we also state and outline
the proof of a sharp delay-independent global stability result\, showing
that it works for our main examples. The interplay between the continuous
dynamical system generated by the delay equation and an associated one-d
imensional discrete dynamical system plays an essential role in our approa
ch.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Geyer (TU Delft)
DTSTART:20210517T140000Z
DTEND:20210517T150000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/21
DESCRIPTION:Title: Stability and persistence of periodic traveling waves\nb
y Anna Geyer (TU Delft) as part of UAB dynamical systems group internation
al seminar\n\n\nAbstract\nIn the first part of my talk\, I will present a
result on the stability of smooth periodic traveling waves of the Camassa-
Holm equation. This equation models the propagation of shallow water waves
and has been studied extensively. The problem of spectral stability of pe
riodic waves however was still open. The key to obtaining the spectral sta
bility is that the periodic waves can be characterised by an alternative H
amiltonian structure\, different from the standard formulation.\n\nIn the
second part of my talk\, I will focus on the problem of persistence of per
iodic traveling waves in Hamiltonian PDE (for instance\, the Camassa-Holm
equation) under perturbations. I will show that the number of traveling w
aves that persist are controlled by the zeros of certain Abelian integrals
. Moreover we will see that one can design the perturbations precisely so
that any prescribed number of traveling waves persists.\n\nThe first part
is joint work with Dmitry Pelinovsky and Fabio Natali\, the second part wi
th Armengol Gasull and Víctor Mañosa\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaume Llibre (Universitat Autònoma de Barcelona)
DTSTART:20210531T100000Z
DTEND:20210531T110000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/22
DESCRIPTION:Title: Results and open problems on the algebraic limit cycles of t
he planar polynomial differential systems\nby Jaume Llibre (Universita
t Autònoma de Barcelona) as part of UAB dynamical systems group internati
onal seminar\n\n\nAbstract\nIn this talk we summarize some results and ope
n problems on the algebraic limit cycles of the planar polynomial differen
tial systems. More precisely\,\n\n 1.- we study the maximum number of a
lgebraic limit cycles of the polynomial differential differential systems
of degree n\;\n\n 2.- we show how to use the algebraic limit cycles for
proving that any finite configuration of limit cycles can be realized by
some polynomial differential system\;\n\n 3.- we provide the maximum nu
mber of algebraic limit cycles formed by circles that a polynomial differe
ntial system of degree $n$ can exhibit\;\n\n 4.- we study the algebraic
limit cycles of the polynomial differential systems of degree 2.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Misiurewicz (Purdue University Indianapolis)
DTSTART:20210531T141000Z
DTEND:20210531T151000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/23
DESCRIPTION:Title: Flexibility of entropies for piecewise expanding unimodal ma
ps\nby Michal Misiurewicz (Purdue University Indianapolis) as part of
UAB dynamical systems group international seminar\n\n\nAbstract\nWe invest
igate the flexibility of the entropy (topological and metric) for the clas
s of piecewise expanding unimodal maps. We show that the only restrictions
for the values of the topological and metric entropies in this class are
that both are positive\, the topological entropy is at most log 2\, and th
e metric entropy is not larger than the topological entropy. In order to h
ave a better control on the metric entropy\, we work mainly with topologic
ally mixing piecewise expanding skew tent maps\, for which there are only
2 different slopes. For those maps\, there is an additional restriction th
at the topological entropy is larger than (1/2) log 2. Moreover\, we gener
alize and give a different interpretation of the Milnor-Thurston formula c
onnecting the topological entropy and the kneading determinant for unimoda
l maps.\nThis is joint work with Lluís Alsedà and Rodrigo Pérez.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dierk Schleicher (Institut de Mathématiques de Marseille)
DTSTART:20210419T133000Z
DTEND:20210419T143000Z
DTSTAMP:20260404T111134Z
UID:SeminarGSDUAB/24
DESCRIPTION:Title: Finding polynomial roots using complex analysis\, dynamical
systems\, computer algebra\nby Dierk Schleicher (Institut de Mathémat
iques de Marseille) as part of UAB dynamical systems group international s
eminar\n\n\nAbstract\nOne of the classical problems in all areas of mathem
atics is to find roots of complex polynomials. It is well known that this
can be done only by methods of approximation. We discuss three classical m
ethods: the Newton\, Weierstrass\, and Ehrlich-Aberth methods\; these are
complex analytic maps that\, under iteration\, are supposed to converge to
one root\, resp. all roots of the polynomial. Locally\, these methods con
verge fast\, but the global dynamical properties are hard to describe.\nWe
introduce these complex analytic dynamical systems and describe recent pr
ogress towards their global dynamical properties. In particular\, the Newt
on and Weierstrass methods are not globally convergent: for open sets of p
olynomials there are open sets of initial points that fail to converge to
roots. Moreover\, for Weierstrass and Ehrlich-Aberth\, there are orbits th
at are always defined and converge\, but not to roots. For Newton\, there
is meanwhile a rich theory about its global dynamics\, but there are many
open questions for all these methods.\nMuch of this is joint work with mem
bers of my ERC team\, in particular my PhD student Bernhard Reinke (who wi
ll present more details on Thursday)\, as well as with colleagues.\n
LOCATION:https://stable.researchseminars.org/talk/SeminarGSDUAB/24/
END:VEVENT
END:VCALENDAR