Speaker: 王毅教授，中国科学技术大学数学科学学院

Title: "Almost-sure" Poincare-Bendixson Theorem and Invariant Cones of Rank-2

Language: Chinese 

Time & Venue: 2025.01.08 19:00-20:00  腾讯会议：846-508-908（会议密码：250108）

Abstract: The Poincare-Bendixson Theorem is a fundamental Theorem for 2-dimensional systems of ODEs, asserting that any compact omega-limit set devoid of equilibrium points is characterized by a single closed trajectory. In this talk, we will delve into the Poincare-Bendixson Type property within the context of higher-dimensional systems and explore its intimate connection with invariant cones of rank-2. We will show that, within this framework, the vast majority of orbits (under both topological and measure-theoretic perspectives) will exhibit the Poincare-Bendixson Type property.