Abstract
We briefly survey the theory of thermodynamic formalism for uniformly hyperbolic systems, and then describe several recent approaches to the problem of extending this theory to non-uniform hyperbolicity. The first of these approaches involves Markov models such as Young towers, countable-state Markov shifts, and inducing schemes. The other two are less fully developed but have seen significant progress in the last few years: these involve coarse-graining techniques (expansivity and specification) and geometric arguments involving push-forward of densities on admissible manifolds.
Original language | English (US) |
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Pages (from-to) | 37-82 |
Number of pages | 46 |
Journal | Arnold Mathematical Journal |
Volume | 3 |
Issue number | 1 |
DOIs | |
State | Published - Apr 1 2017 |
All Science Journal Classification (ASJC) codes
- General Mathematics