Lyapunov Exponents of Linear Cocycles Over Markov Shifts

TL;DR

This paper demonstrates that the Lyapunov exponents of linear cocycles over Markov shifts vary continuously with changes in the matrix coefficients and transition probabilities.

Contribution

It establishes the continuity of Lyapunov exponents for GL(2)-cocycles over Markov shifts with respect to underlying data.

Findings

Lyapunov exponents depend continuously on matrix coefficients.

Lyapunov exponents depend continuously on Markov measure transition probabilities.

Continuity holds for GL(2)-cocycles over Markov shifts.

Abstract

The Lyapunov exponents of GL(2)-cocycles over Markov shifts depend continuously on the underlying data, that is, on the matrix coefficients and the Markov measure transition probabilities.