论文标题
强链复发集的Conley型Lyapunov函数
A Conley-type Lyapunov function for the strong chain recurrent set
论文作者
论文摘要
令$ ϕ：x \ times \ mathbb {r} \ rightarrow x $是紧凑型公制空间$（x，d）$的连续流。在本文中，我们建设性地证明了$ ϕ $的连续lyapunov函数的存在，该函数严格降低了$ \ mathcal {scr} _d _d（ϕ）$。这样的结果概括了康利（Conley）对强链复发集的动力学系统的基本定理。
Let $ϕ:X\times\mathbb{R} \rightarrow X$ be a continuous flow on a compact metric space $(X,d)$. In this article we constructively prove the existence of a continuous Lyapunov function for $ϕ$ which is strictly decreasing outside $\mathcal{SCR}_d(ϕ)$. Such a result generalizes Conley's Fundamental Theorem of Dynamical Systems for the strong chain recurrent set.
