# SRB measures and Young towers for surface diffeomorphisms

## TL;DR

This paper establishes geometric conditions for the existence of SRB measures in surface diffeomorphisms, proving a version of the Viana conjecture, and introduces a novel method for constructing Young towers for hyperbolic measures.

## Contribution

It provides necessary and sufficient geometric conditions for SRB measures and introduces a new approach to constructing Young towers for hyperbolic measures.

## Key findings

- Characterization of SRB measures via geometric conditions
- Construction of Young towers for hyperbolic measures
- A new method for hyperbolic branches and shadowing in nonuniform hyperbolicity

## Abstract

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.