# American Institute of Mathematical Sciences

July  1997, 3(3): 433-438. doi: 10.3934/dcds.1997.3.433

## Expansion rates and Lyapunov exponents

 1 Department of Mathematics, University of California, Berkeley, CA, United States

Received  June 1996 Published  April 1997

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 effects of conjugacies on expansion rates are investigated.
Citation: Sebastian J. Schreiber. Expansion rates and Lyapunov exponents. Discrete & Continuous Dynamical Systems - A, 1997, 3 (3) : 433-438. doi: 10.3934/dcds.1997.3.433
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