Oseledets splitting and invariant manifolds on fields of Banach spaces

TL;DR

This paper establishes a semi-invertible Oseledets theorem for cocycles on measurable fields of Banach spaces and applies it to invariant manifold theory, broadening the scope of dynamical systems analysis.

Contribution

It introduces a semi-invertible Oseledets theorem for Banach space cocycles and derives an invariant manifold theorem for nonlinear cocycles in this setting.

Findings

Proved a semi-invertible Oseledets theorem for Banach space cocycles.

Established an invariant manifold theorem for nonlinear cocycles.

Extended dynamical systems theory to measurable fields of Banach spaces.

Abstract

We prove a semi-invertible Oseledets theorem for cocycles acting on measurable fields of Banach spaces, i.e. we only assume invertibility of the base, not of the operator. As an application, we prove an invariant manifold theorem for nonlinear cocycles acting on measurable fields of Banach spaces.