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Dimension, entropy and Lyapunov exponents

Published online by Cambridge University Press:  13 August 2009

Lai-Sang Young
Lai-Sang Young
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824
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Abstract

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We consider diffeomorphisms of surfaces leaving invariant an ergodic Borel probability measure μ. Define HD (μ) to be the infimum of Hausdorff dimension of sets having full μ-measure. We prove a formula relating HD (μ) to the entropy and Lyapunov exponents of the map. Other classical notions of fractional dimension such as capacity and Rényi dimension are discussed. They are shown to be equal to Hausdorff dimension in the present context.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 1 , March 1982 , pp. 109 - 124
Copyright
Copyright © Cambridge University Press 1982

References

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