SRB measures and Young towers for surface diffeomorphisms
| Autor: | Yakov Pesin, Vaughn Climenhaga, Stefano Luzzatto |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Nuclear and High Energy Physics
Pure mathematics Conjecture Mathematics::Dynamical Systems 37D25 (primary) 37C40 37E30 (secondary) 010102 general mathematics Statistical and Nonlinear Physics Dynamical Systems (math.DS) Surface (topology) 01 natural sciences Measure (mathematics) Tower (mathematics) Nonlinear Sciences::Chaotic Dynamics Alpha (programming language) 0103 physical sciences FOS: Mathematics 0101 mathematics Mathematics - Dynamical Systems 010306 general physics Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.1904.00034 |
| Popis: | We give geometric conditions that are necessary and sufficient for the existence of Sinai-Ruelle-Bowen (SRB) measures for $C^{1+\alpha}$ surface diffeomorphisms, thus proving a version of the Viana conjecture. As part of our argument we give an original method for constructing first return Young towers, proving that every hyperbolic measure, and in particular every SRB measure, can be lifted to such a tower. This method relies on a new general result on hyperbolic branches and shadowing for pseudo-orbits in nonuniformly hyperbolic sets which is of independent interest. Comment: Identical to v2 except that some blue text marking previous edits has been reverted to black |
| Databáze: | OpenAIRE |
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