Hölder continuity of Oseledets splittings for semi-invertible operator cocycles

Abstract

For Hölder continuous cocycles over an invertible, Lipschitz base, we establish the Hölder continuity of Oseledets subspaces on compact sets of arbitrarily large measure. This extends a result of Araújo, Bufetov, and Filip by considering possibly noninvertible cocycles, which in addition may take values in the space of compact operators on a Hilbert space. As a by-product of our work, we also show that a noninvertible cocycle with nonvanishing Lyapunov exponents exhibits nonuniformly hyperbolic behaviour (in the sense of Pesin) on a set of full measure.

Minor revisions to match accepted version in ETDS

References in corpus (2)

• On Hoelder-continuity of Oseledets subspaces
• Entropy, volume growth and SRB measures for Banach space mappings

Cited by in corpus (9)

• A spectral approach for quenched limit theorems for random expanding dynamical systems
• Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles
• Regularity of characteristic exponents and linear response for transfer operator cocycles
• On the periodic approximation of Lyapunov exponents for semi-invertible cocycles
• On the linearization of infinite-dimensional random dynamical systems
• Periodic approximation of Oseledets subspaces for semi-invertible cocycles
• 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