Abstract
We give geometric conditions that are necessary and sufficient for the existence of Sinai–Ruelle–Bowen (SRB) measures for C1+α 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 non-uniformly hyperbolic sets which is of independent interest.
Original language | English (US) |
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Pages (from-to) | 973-1059 |
Number of pages | 87 |
Journal | Annales Henri Poincare |
Volume | 23 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2022 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics