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Symbolic dynamics for non-uniformly hyperbolic systems

Published online by Cambridge University Press:  17 December 2020

YURI LIMA*
Affiliation:
Yuri Lima, Departamento de Matemática, Universidade Federal do Ceará (UFC), Campus do Pici, Bloco 914, CEP 60440-900. Fortaleza – CE, Brazil (e-mail: yurilima@gmail.com)

Abstract

This survey describes the recent advances in the construction of Markov partitions for non-uniformly hyperbolic systems. One important feature of this development comes from a finer theory of non-uniformly 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.

Type
Survey Article
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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