中科院数学与系统科学研究院
数学研究所
动力系统研究中心
学术报告会
报告人：Prof. Kening Lv（BYU）
题 目：SRB Measures for A Class of Partially Hyperbolic Attractors in Hilbert spaces
时 间：12.11（星期四）, 15:00--16:00
地 点：数学院南楼N913室
摘要：
We study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space. We show several results including (i) if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has at least one SRB measure; (ii) if the attractor is uniformly hyperbolic and the system is topological mixing and the splitting is H\"older continuous, then there exists a unique SRB measure which is mixing; (iii) if the attractor is uniformly hyperbolic and the system is non-wondering and and the splitting is H\"older continuous, then there exists at most finitely many SRB measures; (iv) for a given hyperbolic measure, there exist at most countably many ergodic components whose basin contains an observable set. This is a joint work with Zeng Lian and Pei-Dong Liu.