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The essential coexistence phenomenon in Hamiltonian dynamics

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Yakov Pesin
Penn State University
Tue, 2018-05-29 15:00 - 16:00
MPIM Seminar Room

I will discuss a phenomenon of the essential coexistence of regular (zero Lyapunov exponents and hence, zero entropy) dynamics and chaotic (non-zero Lyapunov exponents and positive entropy) dynamics in the setting of smooth dynamical systems. I will review some recent results in this direction, discuss some open problems and describe some new examples of essential coexistence. In particular, I will outline a construction of a Hamiltonian system which demonstrate a "complete? KAM-type picture of coexistence of invariant KAM tori and surrounding "chaotic sea".

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