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Topological entropy for noncompact sets
Open accessAbstract
For f : X → X continuous and Y ⊂ X a topological entropy h ( f , Y ) is defined. For X compact one obtains results generalizing known theorems about entropy for compact Y and about Hausdorff dimension for certain Y ⊂ X = S 1 . A notion of entropy-conjugacy is proposed for homeomorphisms.
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Cited by
Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
Barreira, L., & Schmeling, J. (2000) · Israel Journal of Mathematics · doi:10.1007/bf02773211 · Cited by 349
Thermodynamic formalism for countable Markov shifts
SARIG, O. M. (1999) · Ergodic Theory and Dynamical Systems · doi:10.1017/s0143385799146820 · Cited by 329
On the measure of maximal entropy for finite horizon Sinai Billiard maps
Baladi, V., & Demers, M. (2020) · Journal of the American Mathematical Society · doi:10.1090/jams/939 · Cited by 31
A Geometric Approach to Semi-Dispersing Billiards
Burago, D., Ferleger, S., & Kononenko, A. (2000) · Encyclopaedia of Mathematical Sciences · doi:10.1007/978-3-662-04062-1_2 · Cited by 21
Metadata
- Authors
- Bowen, R.
- Venue
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1973
- Volume
- 184
- Issue
- 0
- Pages
- 125-136
- ISSN
- 0002-9947 (ISSN-L)
- 1088-6850
- OpenAlex
- W1999578955
- Cited by
- 581
- References
- 0
- FWCI
- 0.81
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Bowen, R. (1973). Topological entropy for noncompact sets. Transactions of the American Mathematical Society. https://doi.org/10.1090/s0002-9947-1973-0338317-x
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
