Non-Uniform hyperbolicity for infinite dimensional cocycles

TL;DR

This paper demonstrates that non-uniformly Anosov cocycles are densely prevalent among certain infinite-dimensional dynamical systems, specifically in partially hyperbolic skew products with non-trivial unstable bundles.

Contribution

It establishes the C0-density of non-uniformly Anosov cocycles in the space of partially hyperbolic infinite-dimensional skew products.

Findings

Non-uniformly Anosov cocycles are C0-dense in the specified family.

The result applies to systems with non-trivial unstable bundles.

The setting involves infinite-dimensional Hilbert spaces and ergodic measures.

Abstract

Let H be an infinite dimensional separable Hilbert space, X a compact Hausdorff space and f : X \rightarrow X a homeomorphism which preserves a Borel ergodic measure which is positive on non-empty open sets. We prove that the non-uniformly Anosov cocycles are C0-dense in the family of partially hyperbolic f,H-skew products with non-trivial unstable bundles.