Expansion rates and Lyapunov exponents

Sebastian J. Schreiber

doi:10.3934/dcds.1997.3.433

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1997, Volume 3, Issue 3: 433-438. Doi: 10.3934/dcds.1997.3.433

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Expansion rates and Lyapunov exponents

Sebastian J. Schreiber^1,

1.
Department of Mathematics, University of California, Berkeley, CA

Received: May 31, 1996

Published: June 1997

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Abstract

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.

Keywords:

Lyapunov exponents,
expansion rates.

Mathematics Subject Classification: 35Cxx.

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