Estimating invariant measures and Lyapunov exponents

Abstract

This paper describes a method for obtaining rigorous numerical bounds on time averages for a class of one-dimensional expanding maps. The idea is to directly estimate the absolutely continuous invariant measure for these maps, without computing trajectories. The main theoretical result is a bound on the convergence rate of the Frobenius-Perron operator for such maps. The method is applied to estimate the Lyapunov exponents for a planar map of recent interest.