走向现代数学学术报告 - 夏明洋博士（No. 721）

报告题目：Semi-conjugacy rigidity for endomorphisms derived from Anosov

报 告 人：夏明洋 博士（南方科技大学）

报告时间：2024年6月20日（星期四）15:30

地点：东海岸校区-D实209

摘要：Differing from the case of diffeomorphisms derived from Anosov, there is no a priori semi-conjugacy on the torus between $f$ and its linearization in the non-invertible case. We show that the endomorphism $f$ is semi-conjugate to its linearization on the 2-torus if and only if $f$ admits the partially hyperbolic splitting with two $Df$-invariant subbundles. Moreover, if $f$ has the unstable subbundle, we prove the semi-conjugacy is exactly a topological conjugacy, and the center Lyapunov exponents of periodic points of $f$ coincide and equal to the stable Lyapunov exponent of its linearization. In particular, $f$ is an Anosov endomorphism and the conjugacy is smooth along the stable foliation. For the case that $f$ has the stable subbundle, we get that there is still some rigidity on its stable Lyapunov exponents. However, we also give examples that the semi-conjugacy is indeed non-injective. Finally, we present some applications for the conservative case. This is a joint work with Ruihao Gu.

报告人简介：夏明洋，博士毕业于北京大学，现在南方科技大学数学系从事博士后研究工作。主要研究方向是微分动力系统，在Sci. China Math.、Discrete Contin. Dyn. Syst.等学术期刊发表论文，获中国博士后科学基金面上项目资助。