Dynamics of products of nonnegative matrices

Abstract

The aim of this manuscript is to understand the dynamics of products of nonnegative matrices. We extend a well known consequence of the Perron-Frobenius theorem on the periodic points of a nonnegative matrix to products of finitely many nonnegative matrices associated to a word and later to products of nonnegative matrices associated to a word, possibly of infinite length.

Keywords

• Products of nonnegative matrices
• common eigenvectors
• common periodic points
• orbits of infinite matrix products