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PRODID:Mathematics Seminar Calendar
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UID:20230321T050222-31520@math.msu.edu
DTSTAMP:20230321T050222Z
SUMMARY:Application of KAM Theory in the Fermi-Ulam Models (cont'd)
DESCRIPTION:Speaker\: Jing Zhou, Penn State University\r\nIn this talk I’ll briefly introduce the Fermi acceleration problem and some existing results on the subject. In particular, I’ll discuss how KAM theory has been applied in several variants of the Fermi-Ulam models. I’ll also discuss some open problems in this direction.
LOCATION:C304 Wells Hall
DTSTART:20221219T190000Z
DTEND:20221219T200000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=31520
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UID:20230321T050222-31552@math.msu.edu
DTSTAMP:20230321T050222Z
SUMMARY:Lorenz attractor and singular flows: expansivity, entropy, and equilibrium states
DESCRIPTION:Speaker\: Fan Yang, Michigan State University\r\n
LOCATION:C304 Wells Hall
DTSTART:20230120T200000Z
DTEND:20230120T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=31552
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UID:20230321T050222-31566@math.msu.edu
DTSTAMP:20230321T050222Z
SUMMARY:Foliations and transverse invariant measures from a dynamical systems point of view
DESCRIPTION:Speaker\: Fan Yang, Michigan State University\r\nIn this talk, we will discuss foliations and their transverse invariant measures (i.e., measures on cross-sections that are invariant under the holonomy maps) from a dynamical systems point of view. We will show that for a large family of diffeomorphisms, the unstable foliations admit families of transverse measures that are naturally related to certain probability measures invariant under the dynamics. Given an unstable leaf, we will consider a dynamically defined average that captures its intersection with cross-sections and prove that this averaging will converge exponentially fast to the transverse invariant measures. This is a joint work with Ures, Viana and J. Yang.
LOCATION:C117 Wells Hall
DTSTART:20230209T200000Z
DTEND:20230209T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=31566
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UID:20230321T050222-31577@math.msu.edu
DTSTAMP:20230321T050222Z
SUMMARY:Periodic data and smooth rigidity for hyperbolic automorphisms on torus
DESCRIPTION:Speaker\: Zhenqi Wang, Michigan State University\r\nWe study the regularity of the conjugacy between an irreducible Anosov automorphism $A$\r\non torus and its small perturbation $f$.\r\nWe say that $f$ and $A$ has the same periodic data if the\r\nderivatives of the return maps of $f$ and $A$ at the corresponding periodic points are\r\nconjugate. We demonstrate that if $f$ is a $C^s$ diffeomorphism with $s$ sufficiently large and has the same periodic data as $A$, then the conjugacy is $C^{s-\epsilon}$. This completes the characterization of the most elementary $C^1$-invariant for local smooth rigidity.\r\nWe also give the first example of cocycle rigidity over fibers with conjugate periodic data.
LOCATION:A126 Wells Hall
DTSTART:20230223T200000Z
DTEND:20230223T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=31577
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UID:20230321T050222-32606@math.msu.edu
DTSTAMP:20230321T050222Z
SUMMARY: Quasi-stability for partially hyperbolic diffeomorphisms
DESCRIPTION:Speaker\: Huyi Hu, Michigan State University\r\nThe motivation of the work is to study topological properties of\r\npartially hyperbolic systems which are similar to those of uniformly hyperbolic systems. We try to obtain some properties similar to these of uniformly hyperbolic systems by ``ignoring'' the motions along the center direction.\r\n\r\nWe show that any partially hyperbolic systems are quasi-stable in the sense that for any homeomorphism $g$ $C^0$-close to $f$, there exist a continuous map $\pi$ from $M$ to itself and a family of locally defined continuous maps $\{\tau_x\}$, which send points along the center direction, such that\r\n$$\pi\circ g=\tau_{fx}\circ f\circ\pi.\r\n$$\r\n\r\n\r\nIn particular, if $f$ has $C^1$ center foliation, then we can make the motion $\tau$ along the center foliation. \r\n\r\nAs application we obtain some continuity properties for topological entropy.
LOCATION:A126 Wells Hall
DTSTART:20230302T200000Z
DTEND:20230302T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=32606
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UID:20230321T050222-32615@math.msu.edu
DTSTAMP:20230321T050222Z
SUMMARY:A countable partition for singular flows
DESCRIPTION:Speaker\: Fan Yang, MSU\r\nIn this talk we consider the entropy theory for singular vector fields with all singularities hyperbolic and non-degenerate. We will construct a countable partition with the property that the metric entropy for any ergodic invariant measure is finite. For singular star flows, we will show that this partition is generating. This is a joint work with Yi Shi and Jiagang Yang.
LOCATION:A126 Wells Hall
DTSTART:20230316T190000Z
DTEND:20230316T200000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=32615
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