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Toward a smooth ergodic theory for infinite dimensional systems

New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015

October 22, 2015 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Lai-Sang Young (New York University, Courant Institute)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords

  • infinite-dimensional dynamical systems

  • Lyapunov exponents

  • Entropy formulas

  • global dynamics

  • ergodic systems

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14379
Abstract

Focusing on settings that are consistent with semi-flows defined by
dissipative parabolic PDEs, I will discuss some first steps toward
building a dynamical systems theory, in particular a theory of chaotic
systems, for maps and semi-flows in Hilbert and Banach spaces.
I will survey known results and present recent progress, including
theorems on Lyapunov exponents, periodic solutions and horseshoes,
entropy formula and SRB measures, and a notion of “almost every”
initial condition that is natural to the underlying dynamics. Technical
differences between finite and infinite dimensions will also be discussed
Supplements No Notes/Supplements Uploaded
Video/Audio Files

14379

H.264 Video 14379.mp4 307 MB video/mp4 rtsp://videos.msri.org/data/000/024/614/original/14379.mp4 Download
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