SRB measure for higher dimensional singular partially hyperbolic flows

TL;DR

This paper establishes the existence and uniqueness of SRB measures for higher-dimensional singular partially hyperbolic flows using thermodynamic formalism, without relying on Poincaré maps.

Contribution

It introduces a novel approach to proving SRB measure existence and uniqueness in higher dimensions without Poincaré sections.

Findings

Proves existence of SRB measure for singular partially hyperbolic flows in dimension ≥ 3

Establishes uniqueness of the SRB measure in this setting

Develops a method based on thermodynamic formalism, bypassing Poincaré maps

Abstract

We prove the existence and uniqueness of the SRB measure for singular partially hyperbolic flow in dimension $d\ge 3$. The proof does not use Poincar\'e sectional maps, but uses basic properties of thermodynamic formalism.