时间：2026年10月23日（周五）15:30-17:00
地点：E14-301
报告人：安徽理工大学 张一威
讲座主题：Typical Periodic Optimization for Dynamical Systems: Symbolic Dynamics
讲座摘要：This talk reviews some recent progress in typical ergodic optimization for symbolic dynamical systems. We introduce a theory of maximizing sets designed to study systems with weak hyperbolicity in which the Mañé cohomology lemma fails. This theory yields a structural theorem identifying the part of the system responsible for robust non-periodic optimization. We then develop this theorem in the setting of symbolic dynamics, showing that, for any shift space, a typical Lipschitz function has a unique maximizing measure that is either periodic or supported on the Markov boundary of the shift space. As a consequence, Contreras' Typical Periodic Optimization Theorem for shifts of finite type extends to a broad class of shift spaces, including all sofic shifts. This is joint work with Wen Huang, Oliver Jenkinson, and Leiye Xu.
