NDLI: Dimension, entropy and Lyapunov exponents

Content Provider	Scilit
Author	Young, Lai-Sang
Copyright Year	1982
Description	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.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5B6962A34BACD4A07EA5C7B6AE539051/S0143385700009615a.pdf/div-class-title-dimension-entropy-and-lyapunov-exponents-div.pdf
Ending Page	124
Page Count	16
Starting Page	109
ISSN	01433857
e-ISSN	14694417
DOI	10.1017/s0143385700009615
Journal	Ergodic Theory and Dynamical Systems
Issue Number	1
Volume Number	2
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	1982-03-01
Access Restriction	Open
Subject Keyword	Ergodic Theory and Dynamical Systems Applied Mathematics Lyapunov Exponents
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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