SRB measures for diffeomorphisms with continuous invariant splittings

TL;DR

This paper investigates the existence of SRB measures for certain C2 diffeomorphisms with continuous invariant splittings, focusing on non-uniform expansion and Lyapunov exponents.

Contribution

It establishes conditions under which SRB measures exist for attractors with Holder continuous invariant splittings lacking domination.

Findings

Proves existence of SRB measures under non-uniform expansion conditions.

Shows SRB measures exist when one bundle has positive measure expansion.

Demonstrates SRB measures when the other bundle has non-positive Lyapunov exponents.

Abstract

We study the existence of SRB measures of C 2 diffeomorphisms for attractors whose bundles admit Holder continuous invariant (non-dominated) splittings. We prove the existence when one subbundle has the non-uniform expanding property on a set with positive Lebesgue measure and the other subbundle admits non-positive Lyapunov exponents on a total probability set.