Classification of expansive attractors on surfaces

TL;DR

This paper proves a conjecture that all nontrivial transitive expansive attractors on compact surfaces are derived from pseudo-Anosov attractors, clarifying the structure of such dynamical systems.

Contribution

It confirms a longstanding conjecture, establishing that all such attractors are derived from pseudo-Anosov systems, thus advancing the classification of surface attractors.

Findings

Confirmed the conjecture for all nontrivial transitive expansive attractors

Established that these attractors are derived from pseudo-Anosov systems

Clarified the structure of expansive attractors on surfaces

Abstract

We prove the conjecture of F. Rodriguez Hertz and J. Rodriguez Hertz (2006) that every nontrivial transitive expansive attractor of a homeomorphism of a compact surface is a derived from pseudo-Anosov attractor.