Lyapunov Exponents, Periodic Orbits and Horseshoes for Mappings of Hilbert Spaces

Zeng Lian, Lai Sang Young

Research output: Contribution to journalArticle

Abstract

We consider smooth (not necessarily invertible) maps of Hilbert spaces preserving ergodic Borel probability measures, and prove the existence of hyperbolic periodic orbits and horseshoes in the absence of zero Lyapunov exponents. These results extend Katok's work on diffeomorphisms of compact manifolds to infinite dimensions, with potential applications to some classes of periodically forced PDEs.

Original languageEnglish (US)
Pages (from-to)1081-1108
Number of pages28
JournalAnnales Henri Poincare
Volume12
Issue number6
DOIs
StatePublished - Sep 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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