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
Location: MSRI: Simons Auditorium
infinite-dimensional dynamical systems
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
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