Time：15:30-17:00, Friday, October 23 2026
Venue：E14-301
Speaker：Yiwei Zhang, Anhui University of Science and Technology
Title：Typical Periodic Optimization for Dynamical Systems: Symbolic Dynamics
Abstract：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.
