Dimension, entropy and Lyapunov exponents

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)109-124
Number of pages16
JournalErgodic Theory and Dynamical Systems
Volume2
Issue number1
DOIs
StatePublished - 1982

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Hausdorff Dimension
Lyapunov Exponent
Entropy
Borel Measure
Diffeomorphisms
Probability Measure
Fractional
Invariant
Context

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Dimension, entropy and Lyapunov exponents. / Young, Lai Sang.

In: Ergodic Theory and Dynamical Systems, Vol. 2, No. 1, 1982, p. 109-124.

Research output: Contribution to journalArticle

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