Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
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Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
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The number of trajectories between fixed initial and final configurations is finite.
“They are, however, finite in number and we expect this to be the case more generally [10-13].”
From State-to-State Cosmology: A New View on the Cosmological Arrow of Time and the Past Hypothesis (2022) · cites this paper as [13]
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Ott, E., Grebogi, C., & Yorke, J. A. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.1196 · Cited by 5,431 · see citing works
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 · see citing works
State-to-State Cosmology: A New View on the Cosmological Arrow of Time and the Past Hypothesis
Deutsch, J. M., & Aguirre, A. (2022) · Foundations of Physics · doi:10.1007/s10701-022-00597-3 · Cited by 3 · see citing works
“There are a number of rigorous results relating HTop to NPO , for discrete time dynamical systems [12, 13].”
Background
- Authors
- Katok, A.
- Affiliations
- University of Maryland, College Park (US)
- Corresponding author
- Katok, Anatole
- Venue
- Publications Mathématiques de l'IHÉS
- Publisher
- MathDoc/Centre Mersenne
- Published
- 1980-12-07
- Volume
- 51
- Pages
- 137-173
- ISSN
- 0073-8301 (ISSN-L)
- 1618-1913
- OpenAlex
- W2040635624
- Cited by
- 935
- References
- 0
- Citations by year
- 2026: 29 · 2025: 50 · 2024: 41 · 2023: 45 · 2022: 42 · 2021: 40 · 2020: 37 · 2019: 47 · 2018: 26 · 2017: 35 · 2016: 54 · 2015: 27 · 2014: 26 · 2013: 28 · 2012: 42
- FWCI
- 6.66
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Publications mathématiques de l IHÉS (publishedVersion)
- French digital mathematics library (Numdam) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Control and Stability of Dynamical Systems
- Keywords
- Lyapunov exponents, topological entropy, periodic orbits, diffeomorphisms, hyperbolic dynamics, ergodic theory
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