Bai-Pollicott Algorithm for Markovian Products of Positive Matrices

Abstract

We consider the problem of estimating the top Lyapunov exponents for Markovian products of positive matrices. We define a new transfer operator as a matrix of classical transfer operators and prove its spectral properties. With the spectral properties, we generalize (and provide a more theoretically rigorous foundation for) an algorithm that was introduced informally by Bai and formally by Pollicott based on dynamical zeta functions.