Ergodic optimization of Birkhoff averages and Lyapunov exponents

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.

Paper for ICM 2018 Proceedings. 21 pages, 1 figure. 3rd version: A few corrections were made