Expansion rates and Lyapunov exponents

Abstract

The logarithmic expansion rate of a positively invariant set for a C1 endomorphism is shown to equal the infimum of the Lyapunov exponents for ergodic measures with support in the invariant set. Using this result, aperiodic flows of the two torus are s hown to have an expansion rate of zero and the effects of conjugacies on expansion rates are investigated.