Dimension, entropy and Lyapunov exponents

Lai Sang Young

doi:10.1017/S0143385700009615

Dimension, entropy and Lyapunov exponents

Lai Sang Young

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	109-124
Number of pages	16
Journal	Ergodic Theory and Dynamical Systems
Volume	2
Issue number	1
DOIs	https://doi.org/10.1017/S0143385700009615
State	Published - Mar 1982

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1017/S0143385700009615

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Dimension, entropy and Lyapunov exponents

Abstract

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