A local ergodic theorem for non-uniformly hyperbolic symplectic maps with singularities

TL;DR

This paper establishes a criterion for local ergodicity in non-uniformly hyperbolic symplectic maps with singularities, extending previous theoretical results to broader classes of dynamical systems.

Contribution

It introduces a new criterion for local ergodicity applicable to non-uniformly hyperbolic symplectic maps with singularities, extending the work of Liverani and Wojtkowski.

Findings

Proves a new criterion for local ergodicity

Extends ergodic theory to systems with singularities

Generalizes previous theorems to broader classes of maps

Abstract

In this paper, we prove a criterion for the local ergodicity of non-uniformly hyperbolic symplectic maps with singularities. Our result is an extension of a theorem of Liverani and Wojtkowski.