Speaker：Raul Ures (Southern University of Science and Technology)

Time：2026-1-14 10:00

Location：Conference Room S105 at Experiment Building at Haiyun Campus

Abstract:

We study surface diffeomorphisms g homotopic to a pseudo-Anosov f having the same topological entropy as f. In this case, Handel proved that g is semiconjugate to f. We will show that this semiconjugacy is monotone; that is, the preimage of every point is connected. Moreover, we prove that g has a unique entropy maximizing measure such that its push-forward is the entropy maximizing measure for f, and this measure is Bernoulli. Moreover, the semiconjugacy is a metric isomorphism between these measures. In case this measure is the area, the semiconjugacy is differentiable a.e.