Classification of expansive attractors on surfaces
In this paper, a topological and dynamical description of expansive attractors on surfaces is obtained. In [Ergodic Theory Dyn. Syst. 26, No. 1, 291--302 (2006; Zbl 1085.37037)], \textit{F. Rodriguez Hertz} and \textit{J. Rodriguez Hertz} conjectured that all transitive expansive attractors are conjugate to either a hyperbolic attractor or a derived from a pseudo-Anosov attractor. Let \(A\) be an attractor for a homeomorphism \(f\) of a compact surface \(M\). Roughly speaking, we say that \(A\) is derived from pseudo-Anosov if there is a pseudo-Anosov surface homeomorphism \(g : S \to S\) which is a factor of \(f : A \to A\). In the paper under review, the above conjecture is proved. To be more precise, it is proved that every non-trivial transitive expansive attractor of a homeomorphism of a compact surface is a derived from pseudo-Anosov attractor.
scientific article; zbMATH DE number 6038240
scientific article