Notes on the Multiplicative Ergodic Theorem

TL;DR

This paper introduces the Oseledets Multiplicative Ergodic Theorem, explaining its fundamental role in dynamical systems and discussing various generalizations based on lecture notes from international summer schools.

Contribution

It provides an accessible introduction and overview of the theorem and its extensions, aiding understanding in the field of dynamical systems.

Findings

Clarifies the statement and significance of the theorem

Summarizes key generalizations and extensions

Serves as an educational resource for researchers

Abstract

The Oseledets Multiplicative Ergodic theorem is a basic result with numerous applications throughout dynamical systems. These notes provide an introduction to this theorem, as well as subsequent generalizations. They are based on lectures at summer schools in Brazil, France, and Russia.