Lyapunov exponents, periodic orbits, and horseshoes for semiflows on Hilbert spaces

By Zeng Lian, Lai-Sang Young. 2012

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Two settings are considered: flows on finite dimensional Riemann- ian manifolds, and semiflows on Hilbert spaces with conditions consistent with those in systems defined by dissipative parabolic PDEs. Under certain assump- tions on Lyapunov exponents and entropy, we prove the existence of geometric structures called horseshoes; this implies in particular the presence of infinitely many periodic solutions. For diffeomorphisms of compact manifolds, analogous results are due to A. Katok. Here we extend Katok’s results to (i) continuous time and (ii) infinite dimensions. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012 E-mail address: lian@cims.nyu.edu Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012 E-mail address: lsy@cims.nyu.edu

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/20b5a7060d210a6ef2724c15cb2e0bfdba23911a