Finite rank approximations of expanding maps with neutral singularities

TL;DR

This paper extends finite rank approximation methods to a class of expanding maps with neutral singularities, enabling analysis of Sinai-Ruelle-Bowen measures beyond hyperbolic systems.

Contribution

It introduces a finite rank approximation scheme applicable to expanding maps with neutral singularities, broadening the scope of previous hyperbolic-only results.

Findings

Finite rank scheme successfully approximates SRB measures in the new class of maps.

Extension of approximation techniques from hyperbolic to neutral singularity systems.

Validation of the scheme's effectiveness through rigorous proofs.

Abstract

For a class of expanding maps with neutral singularities we prove the validity of a finite rank approximation scheme for the analysis of Sinai-Ruelle-Bowen measures. Earlier results of this sort were known only in the case of hyperbolic systems.