Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles

Abstract

We prove that for semi-invertible and Hölder continuous linear cocycles $A$ acting on an arbitrary Banach space and defined over a base space that satisfies the Anosov Closing Property, all exceptional Lyapunov exponents of $A$ with respect to an ergodic invariant measure for base dynamics can be approximated with Lyapunov exponents of $A$ with respect to ergodic measures supported on periodic orbits. Our result is applicable to a wide class of infinite-dimensional dynamical systems.

Revised version following the suggestions of referees. Accepted for publication in Annales Academiae Scientiarum Fennicae

References in corpus (3)

• The generalized Berger-Wang formula and the spectral radius of linear cocycles
• Hölder continuity of Oseledets splittings for semi-invertible operator cocycles
• Periodic approximation of Lyapunov exponents for Banach cocycles

Cited by in corpus (7)

• Hyers-Ulam stability for hyperbolic random dynamics
• Quenched linear response for smooth expanding on average cocycles
• On the linearization of infinite-dimensional random dynamical systems
• Hölder continuity of Oseledets subspaces for linear cocycles on Banach spaces
• Sub-additivity of measure-theoretic entropies of commuting transformations on Banach space
• Characterization of SRB Measures for Random Dynamical Systems in a Banach space
• On the spectral radius of compact operator cocycles