Minicourse in Dynamical Systems——Entropy in differentiable dynamical systems
主 题: Minicourse in Dynamical Systems——Entropy in differentiable dynamical systems
报告人: Prof. Gang Liao (Soochow University)
时 间: 2018-04-20 08:30-12:00
地 点: Room 1556(1560)，Sciences Building No. 1
10:00-10:30 Tea Break Room 1384, Sciences Building No. 1
Abstract: Entropy, as a statistical index, plays a fundamental role in the study of dynamical systems. In this series, we plan to introduce the entropy theory in differentiable dynamical systems. First, we start from the background of entropy and the knowledge for general measurable and topological systems. Then, we consider how the differential structure influences the expressions of entropy. Usually, there are two aspects: (1) hyperbolicity: the better the hyperbolicity, the more uniform the global distribution of orbits; (2) smoothness: the better the smoothness, the more regular the local behavior of orbits. Continuity of entropy, the relationship with Lyapunov exponent, and Yomdin-Gromov semi-algebraic theory will be discussed. Furthermore, we will introduce some recent results and open questions.