BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rafael de la Llave (Georgia Tech) DTSTART:20200506T130000Z DTEND:20200506T140000Z DTSTAMP:20260404T094427Z UID:CDSNS_Virtual/1 DESCRIPTION:Title: Constructive methods in KAM theory: from numerics to regulari ty\nby Rafael de la Llave (Georgia Tech) as part of CDSNS virtual coll oquium on dynamics\n\n\nAbstract\nWe will present the "a-posteriori" appro ach to KAM theory.\n\nWe formulate an invariance equation and show that an approximate-enough solution which verifies some non-degeneracy conditions leads to a solution.  Note that this does not have any reference to inte grable systems and that the non-degeneracy conditions are not global prope rties of the system\, but only properties of the solution. The "automatic reducibility" allows to take advantage of the geometry to develop very eff icient Newton methods and show that they converge.\n\nThis leads to very e fficient numerical  algorithms (which moreover can be proved to\nlead to correct solutions)\, to validate formal expansions. From a more theoretica l point of view\, it can be applied to other geometric contexts (conformal ly symplectic\, presymplectic) and other geometric objects such as whisker ed tori. One can deal well with degenerate systems\, singular perturbation theory and obtain simple proofs of monogenicity and Whitney regularity.\n \nThis is joint work with many people.\n\nThis is the first installment of our Virtual CDSNS Colloquium at Georgia Tech. It will meet online weekly at 9am on Wednesdays.\n LOCATION:https://stable.researchseminars.org/talk/CDSNS_Virtual/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaofeng Su (Georgia Tech) DTSTART:20200513T130000Z DTEND:20200513T140000Z DTSTAMP:20260404T094427Z UID:CDSNS_Virtual/2 DESCRIPTION:Title: Random Young towers\nby Yaofeng Su (Georgia Tech) as part of CDSNS virtual colloquium on dynamics\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/CDSNS_Virtual/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Vilaca Da Rocha (Georgia Tech) DTSTART:20200520T160000Z DTEND:20200520T170000Z DTSTAMP:20260404T094427Z UID:CDSNS_Virtual/3 DESCRIPTION:Title: Riemann's non-differentiable function is intermittent\nby Victor Vilaca Da Rocha (Georgia Tech) as part of CDSNS virtual colloquium on dynamics\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/CDSNS_Virtual/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoît Grébert (Université de Nantes) DTSTART:20200527T130000Z DTEND:20200527T140000Z DTSTAMP:20260404T094427Z UID:CDSNS_Virtual/4 DESCRIPTION:Title: Long-time dynamics for the generalized Korteweg-de Vries and Benjamin-Ono equations\nby Benoît Grébert (Université de Nantes) as part of CDSNS virtual colloquium on dynamics\n\n\nAbstract\nWe provide an accurate description of the long time dynamics for generalized Korteweg-d e Vries and Benjamin-Ono equations on the circle without external paramet ers and for almost any (in probability and in density) small initial datum . To obtain that result we construct for these two classes of equations an d under a very weak hypothesis of non degeneracy of the nonlinearity\, rat ional normal forms on open sets surrounding the origin in high Sobolev reg ularity. With this new tool we can make precise the long time dynamics of the respective flows. In particular we prove a long-time stability result in Sobolev norm: given a large constant M and a sufficiently small paramet er ε\, for generic initial datum u(0) of size ε\, we control the Sobolev norm of the solution u(t) for time of order ε^{−M}.\n LOCATION:https://stable.researchseminars.org/talk/CDSNS_Virtual/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Jason Mireles-James (Florida Atlantic University) DTSTART:20200603T130000Z DTEND:20200603T140000Z DTSTAMP:20260404T094427Z UID:CDSNS_Virtual/5 DESCRIPTION:Title: Parameterization of unstable manifolds for delay differential equations\nby Jason Mireles-James (Florida Atlantic University) as pa rt of CDSNS virtual colloquium on dynamics\n\n\nAbstract\nDelay differenti al equations (DDEs) are important in physical applications where there is a time lag in communication between subsystems. From a mathematical point of view DDEs are an interesting source of problems as they provide natura l examples of infinite dimensional dynamical systems. I'll discuss some s pectral numerical methods for computing invariant manifolds for DDEs and p resent some applications.\n LOCATION:https://stable.researchseminars.org/talk/CDSNS_Virtual/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Tanzi (New York University) DTSTART:20200701T130000Z DTEND:20200701T140000Z DTSTAMP:20260404T094427Z UID:CDSNS_Virtual/6 DESCRIPTION:Title: Nonuniformly hyperbolic systems arising from coupling of chao tic and gradient-like systems\nby Matteo Tanzi (New York University) a s part of CDSNS virtual colloquium on dynamics\n\n\nAbstract\nWe investiga te dynamical systems obtained by coupling an Anosov diffeomorphism and a N-pole-to-S-pole map of the circle. Both maps are uniformly hyperbolic\; h owever\, they have contrasting character\, as the first one is chaotic whi le the second one has “orderly" dynamics. The first thing we show is tha t even weak coupling can produce interesting phenomena: when the attractor of the uncoupled system is not normally hyperbolic\, most small interacti ons transform it from a smooth surface to a fractal-like set. We then con sider stronger couplings in which the action of the Anosov diffeomorphism on the circle map has certain monotonicity properties. These couplings pro duce genuine obstructions to uniform hyperbolicity\; however\, the monoton icity conditions make the system amenable to study by leveraging techniqu es from the geometric and ergodic theories of hyperbolic systems. In part icular\, we can show existence of invariant cones and SRB measures. \n\nTh is is joint work with Lai-Sang Young.\n LOCATION:https://stable.researchseminars.org/talk/CDSNS_Virtual/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Caroline Wormell (University of Sydney) DTSTART:20200617T130000Z DTEND:20200617T140000Z DTSTAMP:20260404T094427Z UID:CDSNS_Virtual/7 DESCRIPTION:Title: Spectral Galerkin transfer operator methods in uniformly-expa nding dynamics\nby Caroline Wormell (University of Sydney) as part of CDSNS virtual colloquium on dynamics\n\n\nAbstract\nFull-branch uniformly expanding maps and their long-time statistical quantities are commonly use d as simple models in the study of chaotic dynamics\, as well as being of their own mathematical interest. A wide range of algorithms for computing these quantities exist\, but they are typically unspecialised to the high- order differentiability of many maps of interest\, and so have a weak trad eoff between computational effort and accuracy.\n\nThis talk will cover a rigorous method to calculate statistics of these maps by discretising tran sfer operators in a Chebyshev polynomial basis. This discretisation is hig hly efficient: I will show that\, for analytic maps\, numerical estimates obtained using this discretisation converge exponentially quickly in the o rder of the discretisation\, for a polynomially growing computational cost . In particular\, it is possible to produce (non-validated) estimates of m ost statistical properties accurate to 14 decimal places in a fraction of a second on a personal computer. Applications of the method to the study o f intermittent dynamics and the chaotic hypothesis will be presented.\n LOCATION:https://stable.researchseminars.org/talk/CDSNS_Virtual/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Bhanu Kumar (Georgia Tech) DTSTART:20200708T160000Z DTEND:20200708T170000Z DTSTAMP:20260404T094427Z UID:CDSNS_Virtual/8 DESCRIPTION:Title: Rapid and Accurate Computation of Invariant Tori\, Manifolds\ , and Connections Near Mean Motion Resonances in Periodically Perturbed Pl anar Circular Restricted 3-Body Problem Models\nby Bhanu Kumar (Georgi a Tech) as part of CDSNS virtual colloquium on dynamics\n\n\nAbstract\nWhe n the planar circular restricted 3-body problem (RTBP) is periodically per turbed\, most unstable resonant periodic orbits become invariant tori. In this study\, we 1) develop a quasi-Newton method which simultaneously solv es for the tori and their center\, stable\, and unstable directions\; 2) i mplement continuation by both perturbation parameter as well as rotation n umbers\; 3) compute Fourier-Taylor parameterizations of the stable and uns table manifolds\; 4) globalize these manifolds\; and 5) compute homoclinic and heteroclinic connections. Our methodology improves on efficiency and accuracy compared to prior studies\, and applies to a variety of periodic perturbations. We demonstrate the tools on the planar elliptic RTBP. This is based on joint work with R. Anderson and R. de la Llave.\n LOCATION:https://stable.researchseminars.org/talk/CDSNS_Virtual/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Lewis Bowen (UT Austin) DTSTART:20200722T130000Z DTEND:20200722T140000Z DTSTAMP:20260404T094427Z UID:CDSNS_Virtual/9 DESCRIPTION:Title: A von Neumann algebra valued Multiplicative Ergodic Theorem\nby Lewis Bowen (UT Austin) as part of CDSNS virtual colloquium on dyna mics\n\n\nAbstract\nIn 1960\, Furstenberg and Kesten introduced the proble m of describing the asymptotic behavior of products of random matrices as the number of factors tends to infinity. Oseledets’ proved that such pro ducts\, after normalization\, converge almost surely. This theorem has wid e-ranging applications to smooth ergodic theory and rigidity theory. It ha s been generalized to products of random operators on Banach spaces by Rue lle and others. I will explain a new infinite-dimensional generalization b ased on von Neumann algebra theory which accommodates continuous Lyapunov distribution. No knowledge of von Neumann algebras will be assumed. This i s joint work with Ben Hayes (U. Virginia) and Yuqing Frank Lin (UT Austin\ , Ben-Gurion U.).\n LOCATION:https://stable.researchseminars.org/talk/CDSNS_Virtual/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuqing Lin (UT Austin) DTSTART:20200721T160000Z DTEND:20200721T170000Z DTSTAMP:20260404T094427Z UID:CDSNS_Virtual/10 DESCRIPTION:Title: Introduction to the classical Multiplicative Ergodic Theorem \nby Yuqing Lin (UT Austin) as part of CDSNS virtual colloquium on dyn amics\n\n\nAbstract\nThis is a gentle introduction to the classical Oseled ets' Multiplicative Ergodic Theorem (MET)\, which can be viewed as either a dynamical version of the Jordan normal form of a matrix\, or a matrix ve rsion of the pointwise ergodic theorem (which itself can be viewed as a ge neralization of the strong law of large numbers). We will also sketch Rag hunathan's proof of the MET and discuss how the MET can be applied to smoo th ergodic theory.\n LOCATION:https://stable.researchseminars.org/talk/CDSNS_Virtual/10/ END:VEVENT END:VCALENDAR