动力系统学术报告    

题目：Dimension theory of endomorphisms of CP^k    

报告人：何焱 助理教授（美国俄克拉荷马大学）    

摘要： Let k \ge 1 be an integer and let f: CP^k \to CP^k be a holomorphic endomorphism of algebraic degree at least 2. Let \nu be an invariant ergodic probability measure with positive Lyapunov exponents. In this talk, we will introduce a volume dimension of the measure \nu which is equivalent to the Hausdorff dimension when k =1 but depends on the dynamics of the map when k \ge 2 to incorporate the non-conformality of holomorphic maps in higher dimensional projective spaces. We prove a generalized Mane-Manning formula relating the dimension, entropy and Lyapunov exponents of \nu. As applications we will characterize the first zero of a pressure function for expanding invariant measure in terms of their volume dimensions. For hyperbolic maps, such zero also coincides with the volume dimension of the Julia set, and with the exponent of a natural (volume-)conformal measure. The talk is based on joint work with Fabrizio Bianchi.

报告人简介：何焱，博士毕业于美国芝加哥大学，师从Danny Calegari教授。曾在卢森堡大学、加拿大多伦多大学等著名高校从事博士后研究。现任美国俄克拉荷马大学助理教授。研究领域为复动力系统，双曲几何和thermodynamic formalism，在Ergodic Theory and Dynamical Systems, Transactions AMS, Math Research Letters等国际知名的学术期刊发表多篇论文。    

报告时间：2025年1月6日（周一）上午10:00 -- 11:00

报告地点：教二楼613    

联系人：王方