BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Chiara Caracciolo (Università degli Studi di Roma "Tor Vergata") DTSTART:20200511T081500Z DTEND:20200511T100000Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/1 DESCRIPTION:Title: Elliptic tori in FPU chains\nby Chiara Caracciolo (Univ ersità degli Studi di Roma "Tor Vergata") as part of Dynamical Systems an d Computations\n\n\nAbstract\nWe revisit an algorithm constructing ellipti c tori via normal form\, that was originally\n designed to apply to planet ary problems. The scheme is adapted to properly work with models of chains of N + 1 particles interacting via anharmonic potentials\, thus covering also the case of FPU lattices. We successfully apply our new algorithm to the construction of 1-dimensional elliptic tori for wide sets of the param eter (i.e.\, the total energy of the system) that rules the size of the pe rturbation in FPU chains with N = 4\, 8. Moreover\, we show the stability of the regions surrounding the 1-dimensional elliptic tori. Finally\, we c ompare our semi-analytical results with those provided by numerical explor ations of the FPU-model dynamics\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Philipe Lessard (McGill University) DTSTART:20200603T140000Z DTEND:20200603T150000Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/2 DESCRIPTION:Title: Rigorous integration of infinite dimensional dynamical syst ems via Chebyshev series\nby Jean-Philipe Lessard (McGill University) as part of Dynamical Systems and Computations\n\n\nAbstract\nIn this talk we introduce recent general methods to rigorously \n\n\ncompute solutions of infinite dimensional Cauchy problems. The idea \n\n\nis to expand the s olutions in time using Chebyshev series \n\n\nand use the contraction mapp ing theorem to construct a neighbourhood \n\n\nabout an approximate soluti on which contains the exact solution of the \n\n\nCauchy problem. We apply the methods to some semi-linear parabolic partial \n\n\ndifferential equa tions (PDEs) and delay differential equations (DDEs).\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriela Estevez (Universidade Federal do Rio de Janeiro) DTSTART:20200528T131500Z DTEND:20200528T150000Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/3 DESCRIPTION:Title: Some recent results on multicritical circle maps\nby Ga briela Estevez (Universidade Federal do Rio de Janeiro) as part of Dynamic al Systems and Computations\n\n\nAbstract\nWe study circle maps with a fin ite number of "inflexive" critical points\, the called multicritical circl e maps. The topology of these maps is well understood. One of the main que stions in one dimensional dynamics is on the conditions that make the topo logy determines the geometry. In this talk\, we will discuss some recent r esults concerning this question for these circle maps.\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Maciej Capinski (AGH) DTSTART:20200616T131500Z DTEND:20200616T150000Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/4 DESCRIPTION:Title: Arnold Diffusion and Stochastic Behaviour\nby Maciej Ca pinski (AGH) as part of Dynamical Systems and Computations\n\n\nAbstract\n We will discuss a construction of a stochastic process on energy levels in perturbed Hamiltonian systems. The method follows from shadowing of dynam ics of two coupled horseshoes. It leads to a family of stochastic processe s\, which converge to a Brownian motion with drift\, as the perturbation p arameter converges to zero. Moreover\, we can obtain any desired values of the drift and variance for the limiting Brownian motion\, for appropriate sets of initial conditions. The convergence is in the sense of the functi onal central limit theorem. We give an example of such construction in the PRE3BP.\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Igors Gorbovickis (Jacobs University Bremen) DTSTART:20201014T121500Z DTEND:20201014T140000Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/5 DESCRIPTION:Title: Critical points of the multipliers in the quadratic family: equidistribution and accumulation\nby Igors Gorbovickis (Jacobs Unive rsity Bremen) as part of Dynamical Systems and Computations\n\n\nAbstract\ nA parameter $c_0\\in\\mathbb C$ in the family of quadratic polynomials $f _c(z)=z^2+c$ is a \\textit{critical point of a period $n$ multiplier}\, if the map $f_{c_0}$ has a periodic orbit of period $n$\, whose multiplier\, viewed as a locally analytic function of $c$\, has a vanishing derivative at $c=c_0$. \nInformation about the location of critical points and criti cal values of the multipliers might play a role in the study of the geomet ry of the Mandelbrot set. \n\nWe will discuss asymptotic behavior of criti cal points of the period $n$ multipliers as $n\\to\\infty$. We will show t hat while the critical points equidistribute on the boundary of the Mandel brot set $\\mathbb M$\, their accumulation set $\\mathcal X$ is strictly l arger than $\\partial\\mathbb M$. \n\nIn order to study the geometry of th e accumulation set $\\mathcal X$\, we will introduce a new family of sets $\\mathcal Y_c$ that relate to $\\mathcal X$ in a somewhat similar way as the filled Julia sets relate to the Mandelbrot set.\n\n\nWe will further s how that the accumulation set $\\mathcal X$ is bounded\, path connected an d contains the Mandelbrot set as a proper subset. This is joint work with Tanya Firsova.\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonguk Yang (Stony Brook University) DTSTART:20201105T124500Z DTEND:20201105T140000Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/6 DESCRIPTION:Title: Polynomials with a Siegel disk of Bounded Type\nby Jong uk Yang (Stony Brook University) as part of Dynamical Systems and Computat ions\n\n\nAbstract\nConsider a polynomial with a rotational domain (called a Siegel disc) of bounded type rotation number. It is known that the Sieg el boundary is a quasi-circle that contains at least one critical point. I n the quadratic case\, this means that the entire post-critical set is tra pped within the Siegel boundary\, where the theory of real analytic circle maps provides us with excellent control. However\, in the higher degree c ase\, there exist multiple critical points. A priori\, these “free” cr itical points may accumulate on the Siegel boundary in a complicated way\, causing extreme distortions in the geometry nearby. In my talk\, I show t hat in fact\, this does not happen\, and that the dynamics of the polynomi al can be fully understood near the Siegel boundary.\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Wolf (City College of New York) DTSTART:20201120T141500Z DTEND:20201120T160000Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/7 DESCRIPTION:Title: Computability of topological pressure on compact shift sp aces beyond finite type\nby Christian Wolf (City College of New York) as part of Dynamical Systems and Computations\n\n\nAbstract\nIn this talk we discuss the computability (in the sense of computable analysis) of the topological pressure P_T(phi) on compact shift spaces X for continuous pot entials phi: X -> R. This question has recently been studied for subshifts of finite type (SFTs) and their factors (Sofic shifts). We develop a fram ework to address the computability of the topological pressure on general shift spaces and apply this framework to coded shifts. In particular\, we prove the computability of the topological pressure for all continuous pot entials on S-gap shifts\, generalized gap shifts\, and Beta shifts. We als o construct shift spaces which\, depending on the potential\, exhibit comp utability and non-computability of the topological pressure. We further sh ow that the generalized pressure function (X\,phi) |-> P_T(X\,phi|_X) is n ot computable for a large set of shift spaces X and potentials phi. Along the way of developing these computability results\, we derive several ergo dic-theoretical properties of coded shifts which are of independent intere st beyond the realm of computability. The topic of the talk is joint work with Michael Burr (Clemson U.)\, Shuddho Das (NYU) and Yun Yang (Virginia Tech).\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jason Mireles James (Florida Atlantic University) DTSTART:20201211T141500Z DTEND:20201211T160000Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/8 DESCRIPTION:Title: Validated Numerics for Morse Indices of Delay Differential Equations\nby Jason Mireles James (Florida Atlantic University) as par t of Dynamical Systems and Computations\n\n\nAbstract\nI will review a lit tle bit some basic ideas about delay differential equations (DDEs)\, in pa rticular that they generate discrete time dynamical systems on an appropri ate function space. Then I'll talk about the problem of obtaining a mathem atically rigorous count on the number of unstable eigenvalues at an equili brium solution (the Morse index). The eigenvalues of a DDE solve a transce ndental characteristic equation\, so that a lower bound on the Morse index is obtained by proving the existence of solutions of this nonlinear equat ion in the open right half of the complex plane. A more delicate question is\, how do know when we have found all the solutions? How do we know when to stop? This is counting problem and I will talk about a couple of diffe rent possible solutions\, including one based on Chebyshev spectral method s. This is joint work with J.P. Lessard.\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandre Rodrigues (Universidade do Porto) DTSTART:20210129T121500Z DTEND:20210129T140000Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/9 DESCRIPTION:Title: Unfolding a Bykov attractor: from an attracting torus to st range attractors\nby Alexandre Rodrigues (Universidade do Porto) as pa rt of Dynamical Systems and Computations\n\n\nAbstract\nIn this talk\, we present a mechanism for the emergence of strange attractors in a two-param etric family of differential equations acting on a three-dimensional spher e. When both parameters are zero\, its flow exhibits an attracting heteroc linic network (Bykov attractor) made by two 1-dimensional and one 2-dimens ional separatrices between two hyperbolic saddles-foci with different Mors e indices.\n\nAfter slightly increasing both parameters\, while keeping th e one-dimensional connections unaltered\, we focus our attention in the ca se where the two-dimensional invariant manifolds of the equilibria do not intersect. We show the existence of many complicated dynamical objects\, r anging from an attracting quasi-periodic torus\, Newhouse sinks to Hénon- like strange attractors\, as a consequence of the Torus Bifurcation Theory (developed by Afraimovich and Shilnikov).\n\nUnder generic and checkable hypotheses\, we conclude that any analytic unfolding of a Hopf-zero singul arity (within an appropriate class) contains strange attractors. We also d iscuss the case of the existence of rank-one strange attractors (developed by Q. Wang and L.-S. Young) for this model.\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Tanya Firsova (Kansas State University) DTSTART:20210416T131500Z DTEND:20210416T151500Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/10 DESCRIPTION:Title: Critical points of the multiplier map: equidistribution an d accumulation\nby Tanya Firsova (Kansas State University) as part of Dynamical Systems and Computations\n\n\nAbstract\nWe study asymptotic prop erties of the critical points of the multiplier map. The multiplier of a n on-parabolic orbit of a map $z\\to z^2+c$ can be extended by means of anal ytic continuation to a multiple-valued algebraic function on the space of quadratic polynomials $z^2+c$. We show that as the period of the periodic orbit increases to infinity\, critical points of the multiplier map equidi stribute on the boundary of the Mandelbrot set. We also prove that the acc umulation set of the critical points of multipliers is larger than the bou ndary of the Mandelbrot set. The accumulation set is a bounded path connec ted set\, and it in fact contains all of the Mandelbrot set. This is a joi nt work with I. Gorbovickis.\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Remus Radu (Uppsala Universitet) DTSTART:20210510T131500Z DTEND:20210510T151500Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/11 DESCRIPTION:Title: Rigidity for complex Hénon maps\nby Remus Radu (Uppsa la Universitet) as part of Dynamical Systems and Computations\n\n\nAbstrac t\nThe forward escaping set of a dissipative complex Hénon map is a well- understood dynamical object. By works of Hubbard & Oberste-Vorth it is bih olomorphic to an universal object: $(C-\\bar{D})\\times C$ factored by a d iscrete group of automorphisms isomorphic to $Z[1/2]/Z$. We use this analy tic description to show that two Hénon maps with biholomorphic escaping s ets are in fact the same. In her work Tanase extended this description of the escaping set to the boundary in order to capture the Julia set and int roduced a one-dimensional invariant set that encodes part of the dynamics of the Hénon map. We show that this invariant is also a rigid object for the Hénon map. This talk is based on joint work with Sylvain Bonnot and R aluca Tanase.\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Raluca Tanase (Uppsala Universitet) DTSTART:20210518T111500Z DTEND:20210518T131500Z DTSTAMP:20260404T094912Z UID:CAPA_UU_SEMINAR/12 DESCRIPTION:Title: On hyperbolicity and partial hyperbolicity in the Hénon f amily\nby Raluca Tanase (Uppsala Universitet) as part of Dynamical Sys tems and Computations\n\n\nAbstract\nWe discuss new regions of hyperbolici ty and partial hyperbolicity for the complex Hénon map and show where the y sit in the parameter space in $C^2$.\n LOCATION:https://stable.researchseminars.org/talk/CAPA_UU_SEMINAR/12/ END:VEVENT END:VCALENDAR