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Dimension, entropy and Lyapunov exponents
Open accessAbstract
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.
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Citations
Cites
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
Katok, A. (1980) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684777 · Cited by 935
Cited by
Determining Lyapunov exponents from a time series
Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(85)90011-9 · Cited by 9,499
Ergodic theory of chaos and strange attractors
Eckmann, J. P., & Ruelle, D. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.617 · Cited by 4,941
The Metric Entropy of Diffeomorphisms: Part II: Relations between Entropy, Exponents and Dimension
Ledrappier, F., & Young, L.-S. (1985) · The Annals of Mathematics · doi:10.2307/1971329 · Cited by 361
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Metadata
- Authors
- Young, L.-S.
- Venue
- Ergodic Theory and Dynamical Systems
- Publisher
- Cambridge University Press (CUP)
- Published
- 1982-03
- Volume
- 2
- Issue
- 1
- Pages
- 109-124
- ISSN
- 0143-3857 (ISSN-L)
- 1469-4417
- OpenAlex
- W2112136864
- Cited by
- 633
- References
- 1
- FWCI
- 14.19
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Young, L.-S. (1982). Dimension, entropy and Lyapunov exponents. Ergodic Theory and Dynamical Systems. https://doi.org/10.1017/s0143385700009615
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