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:20260422T225718Z UID:CDSNS_Virtual/1 DESCRIPTION:Title: Constructive methods in KAM theory: from numerics to regularity\ nby Rafael de la Llave (Georgia Tech) as part of CDSNS virtual colloquium on dynamics\n\n\nAbstract\nWe will present the "a-posteriori" approach to KAM theory.\n\nWe formulate an invariance equation and show that an approx imate-enough solution which verifies some non-degeneracy conditions leads to a solution.  Note that this does not have any reference to integrable systems and that the non-degeneracy conditions are not global properties o f the system\, but only properties of the solution. The "automatic reducib ility" allows to take advantage of the geometry to develop very efficient Newton methods and show that they converge.\n\nThis leads to very efficien t numerical  algorithms (which moreover can be proved to\nlead to correct solutions)\, to validate formal expansions. From a more theoretical point of view\, it can be applied to other geometric contexts (conformally symp lectic\, presymplectic) and other geometric objects such as whiskered 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 Vi rtual CDSNS Colloquium at Georgia Tech. It will meet online weekly at 9am on Wednesdays.\n LOCATION:https://researchseminars.org/talk/CDSNS_Virtual/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaofeng Su (Georgia Tech) DTSTART:20200513T130000Z DTEND:20200513T140000Z DTSTAMP:20260422T225718Z UID:CDSNS_Virtual/2 DESCRIPTION:Title: Random Young towers\nby Yaofeng Su (Georgia Tech) as part of CDS NS virtual colloquium on dynamics\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/CDSNS_Virtual/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Vilaca Da Rocha (Georgia Tech) DTSTART:20200520T160000Z DTEND:20200520T170000Z DTSTAMP:20260422T225718Z 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 dyn amics\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/CDSNS_Virtual/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoît Grébert (Université de Nantes) DTSTART:20200527T130000Z DTEND:20200527T140000Z DTSTAMP:20260422T225718Z UID:CDSNS_Virtual/4 DESCRIPTION:Title: Long-time dynamics for the generalized Korteweg-de Vries and Benjami n-Ono equations\nby Benoît Grébert (Université de Nantes) as part o f CDSNS virtual colloquium on dynamics\n\n\nAbstract\nWe provide an accura te description of the long time dynamics for generalized Korteweg-de Vries and Benjamin-Ono equations on the circle without external parameters and for almost any (in probability and in density) small initial datum. To ob tain that result we construct for these two classes of equations and under a very weak hypothesis of non degeneracy of the nonlinearity\, rational n ormal forms on open sets surrounding the origin in high Sobolev regularity . With this new tool we can make precise the long time dynamics of the res pective flows. In particular we prove a long-time stability result in Sobo lev norm: given a large constant M and a sufficiently small parameter ε\, for generic initial datum u(0) of size ε\, we control the Sobolev norm o f the solution u(t) for time of order ε^{−M}.\n LOCATION:https://researchseminars.org/talk/CDSNS_Virtual/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Jason Mireles-James (Florida Atlantic University) DTSTART:20200603T130000Z DTEND:20200603T140000Z DTSTAMP:20260422T225718Z UID:CDSNS_Virtual/5 DESCRIPTION:Title: Parameterization of unstable manifolds for delay differential equati ons\nby Jason Mireles-James (Florida Atlantic University) as part of C DSNS virtual colloquium on dynamics\n\n\nAbstract\nDelay differential equa tions (DDEs) are important in physical applications where there is a time lag in communication between subsystems. From a mathematical point of vie w DDEs are an interesting source of problems as they provide natural examp les of infinite dimensional dynamical systems. I'll discuss some spectral numerical methods for computing invariant manifolds for DDEs and present some applications.\n LOCATION:https://researchseminars.org/talk/CDSNS_Virtual/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Tanzi (New York University) DTSTART:20200701T130000Z DTEND:20200701T140000Z DTSTAMP:20260422T225718Z UID:CDSNS_Virtual/6 DESCRIPTION:Title: Nonuniformly hyperbolic systems arising from coupling of chaotic and gradient-like systems\nby Matteo Tanzi (New York University) as part of CDSNS virtual colloquium on dynamics\n\n\nAbstract\nWe investigate dyna mical systems obtained by coupling an Anosov diffeomorphism and a N-pole- to-S-pole map of the circle. Both maps are uniformly hyperbolic\; however\ , they have contrasting character\, as the first one is chaotic while the second one has “orderly" dynamics. The first thing we show is that even weak coupling can produce interesting phenomena: when the attractor of the uncoupled system is not normally hyperbolic\, most small interactions tra nsform it from a smooth surface to a fractal-like set. We then consider s tronger couplings in which the action of the Anosov diffeomorphism on the circle map has certain monotonicity properties. These couplings produce ge nuine obstructions to uniform hyperbolicity\; however\, the monotonicity c onditions make the system amenable to study by leveraging techniques from the geometric and ergodic theories of hyperbolic systems. In particular\ , we can show existence of invariant cones and SRB measures. \n\nThis is j oint work with Lai-Sang Young.\n LOCATION:https://researchseminars.org/talk/CDSNS_Virtual/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Caroline Wormell (University of Sydney) DTSTART:20200617T130000Z DTEND:20200617T140000Z DTSTAMP:20260422T225718Z UID:CDSNS_Virtual/7 DESCRIPTION:Title: Spectral Galerkin transfer operator methods in uniformly-expanding d ynamics\nby Caroline Wormell (University of Sydney) as part of CDSNS v irtual colloquium on dynamics\n\n\nAbstract\nFull-branch uniformly expandi ng maps and their long-time statistical quantities are commonly used as si mple models in the study of chaotic dynamics\, as well as being of their o wn mathematical interest. A wide range of algorithms for computing these q uantities exist\, but they are typically unspecialised to the high-order d ifferentiability of many maps of interest\, and so have a weak tradeoff be tween computational effort and accuracy.\n\nThis talk will cover a rigorou s method to calculate statistics of these maps by discretising transfer op erators in a Chebyshev polynomial basis. This discretisation is highly eff icient: I will show that\, for analytic maps\, numerical estimates obtaine d using this discretisation converge exponentially quickly in the order of the discretisation\, for a polynomially growing computational cost. In pa rticular\, it is possible to produce (non-validated) estimates of most sta tistical properties accurate to 14 decimal places in a fraction of a secon d on a personal computer. Applications of the method to the study of inter mittent dynamics and the chaotic hypothesis will be presented.\n LOCATION:https://researchseminars.org/talk/CDSNS_Virtual/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Bhanu Kumar (Georgia Tech) DTSTART:20200708T160000Z DTEND:20200708T170000Z DTSTAMP:20260422T225718Z UID:CDSNS_Virtual/8 DESCRIPTION:Title: Rapid and Accurate Computation of Invariant Tori\, Manifolds\, and C onnections Near Mean Motion Resonances in Periodically Perturbed Planar Ci rcular Restricted 3-Body Problem Models\nby Bhanu Kumar (Georgia Tech) as part of CDSNS virtual colloquium on dynamics\n\n\nAbstract\nWhen the p lanar circular restricted 3-body problem (RTBP) is periodically perturbed\ , most unstable resonant periodic orbits become invariant tori. In this st udy\, we 1) develop a quasi-Newton method which simultaneously solves for the tori and their center\, stable\, and unstable directions\; 2) implemen t continuation by both perturbation parameter as well as rotation numbers\ ; 3) compute Fourier-Taylor parameterizations of the stable and unstable m anifolds\; 4) globalize these manifolds\; and 5) compute homoclinic and he teroclinic connections. Our methodology improves on efficiency and accurac y compared to prior studies\, and applies to a variety of periodic perturb ations. We demonstrate the tools on the planar elliptic RTBP. This is base d on joint work with R. Anderson and R. de la Llave.\n LOCATION:https://researchseminars.org/talk/CDSNS_Virtual/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Lewis Bowen (UT Austin) DTSTART:20200722T130000Z DTEND:20200722T140000Z DTSTAMP:20260422T225718Z 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 dynamics\n\ n\nAbstract\nIn 1960\, Furstenberg and Kesten introduced the problem of de scribing the asymptotic behavior of products of random matrices as the num ber of factors tends to infinity. Oseledets’ proved that such products\, after normalization\, converge almost surely. This theorem has wide-rangi ng applications to smooth ergodic theory and rigidity theory. It has been generalized to products of random operators on Banach spaces by Ruelle and others. I will explain a new infinite-dimensional generalization based on von Neumann algebra theory which accommodates continuous Lyapunov distrib ution. No knowledge of von Neumann algebras will be assumed. This is joint work with Ben Hayes (U. Virginia) and Yuqing Frank Lin (UT Austin\, Ben-G urion U.).\n LOCATION:https://researchseminars.org/talk/CDSNS_Virtual/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuqing Lin (UT Austin) DTSTART:20200721T160000Z DTEND:20200721T170000Z DTSTAMP:20260422T225718Z UID:CDSNS_Virtual/10 DESCRIPTION:Title: Introduction to the classical Multiplicative Ergodic Theorem\nb y Yuqing Lin (UT Austin) as part of CDSNS virtual colloquium on dynamics\n \n\nAbstract\nThis is a gentle introduction to the classical Oseledets' Mu ltiplicative Ergodic Theorem (MET)\, which can be viewed as either a dynam ical version of the Jordan normal form of a matrix\, or a matrix version o f the pointwise ergodic theorem (which itself can be viewed as a generaliz ation of the strong law of large numbers). We will also sketch Raghunatha n's proof of the MET and discuss how the MET can be applied to smooth ergo dic theory.\n LOCATION:https://researchseminars.org/talk/CDSNS_Virtual/10/ END:VEVENT END:VCALENDAR