Symbolic dynamics for nonuniformly hyperbolic systems
Abstract
This survey describes the recent advances in the construction of Markov partitions for nonuniformly hyperbolic systems. One important feature of this development comes from a finer theory of nonuniformly hyperbolic systems, which we also describe. The Markov partition defines a symbolic extension that is finite-to-one and onto a non-uniformly hyperbolic locus, and this provides dynamical and statistical consequences such as estimates on the number of closed orbits and properties of equilibrium measures. The class of systems includes diffeomorphisms, flows, and maps with singularities.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2019
- DOI:
- 10.48550/arXiv.1910.11371
- arXiv:
- arXiv:1910.11371
- Bibcode:
- 2019arXiv191011371L
- Keywords:
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- Mathematics - Dynamical Systems
- E-Print:
- Survey article, 66 pages, 20 figures, to appear in Ergodic Theory Dynam. Systems