Continuity of Lyapunov exponents is equivalent to continuity of Oseledets subspaces

TL;DR

This paper establishes that for semi-invertible continuous cocycles, the continuity of Lyapunov exponents is equivalent to the continuity in measure of the associated Oseledets subspaces, linking spectral and geometric stability.

Contribution

It proves the equivalence between the continuity of Lyapunov exponents and the continuity in measure of Oseledets subspaces for semi-invertible continuous cocycles, a novel theoretical result.

Findings

Lyapunov exponents' continuity is equivalent to Oseledets subspaces' continuity in measure.

Provides a new characterization of stability for semi-invertible cocycles.

Bridges spectral and geometric aspects of cocycle stability.

Abstract

We prove that, for semi-invertible continuous cocycles, continuity of Lyapunov exponents is equivalent to continuity, in measure, of Oseledets subspaces.