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Expansion rates and Lyapunov exponents

The logarithmic expansion rate of a positively invariant set for a C 1 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 shown to have an expansion rate of zero and the eects of conjugacies on expansion rates are investigated.