Monotony of the semiconjugacy for diffeomorphisms homotopic to pseudo-Anosov

：Raul Ures（南方科技大学）
：2026-01-14 10:00
：海韵园实验楼S105

报告人：Raul Ures（南方科技大学）

时  间：2026年1月14日10:00

地  点：海韵园实验楼S105

内容摘要:

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.

个人简介：

Raul Ures completed his PhD studies at IMPA, Rio de Janeiro. He was a professor at the University of the Republic, Uruguay, and is currently a professor at the Southern University of Science and Technology in Shenzhen. He has been selected for China’s national talent initiatives and Shenzhen’s "Peacock Plan" for high-level overseas talents. He has several publications in prestigious journals such as Inventiones Mathematicae, Acta Mathematica, Duke Mathematical Journal, etc. His main research areas are dynamical systems and ergodic theory.

 

联系人：吴伟胜