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

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. © 2011 Springer Basel AG.