Ergodic optimization of Birkhoff averages and Lyapunov exponents

TL;DR

This paper explores the extremal values of dynamical quantities like Birkhoff averages and Lyapunov exponents, focusing on the orbits and measures that achieve these extremal values within ergodic optimization.

Contribution

It provides a discussion of key results and open problems in the ergodic optimization of Birkhoff averages and Lyapunov exponents.

Findings

Analysis of extremal invariant measures

Identification of orbits attaining extremal averages

Discussion of open problems in ergodic optimization

Abstract

Ergodic optimization is the study of extremal values of asymptotic dynamical quantities such as Birkhoff averages or Lyapunov exponents, and of the orbits or invariant measures that attain them. We discuss some results and problems.