On the periodic approximation of Lyapunov exponents for semi-invertible cocycles

TL;DR

This paper demonstrates that for semi-invertible linear cocycles, the Lyapunov exponents associated with ergodic measures can be approximated using Lyapunov exponents calculated at periodic points, bridging a gap in understanding their relationship.

Contribution

It provides a proof that Lyapunov exponents for ergodic measures in semi-invertible cocycles can be approximated by those on periodic points, a novel result in dynamical systems theory.

Findings

Lyapunov exponents of ergodic measures can be approximated by periodic points

The approximation holds for semi-invertible linear cocycles

Establishes a link between ergodic measures and periodic orbit exponents

Abstract

We prove that, for semi-invertible linear cocycles, Lyapunov exponents of ergodic measures may be approximated by Lyapunov exponents on periodic points.