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Let $\phi:X\times\mathbb{R} \rightarrow X$ 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 $\phi$ which… Click to show full abstract
Let $\phi:X\times\mathbb{R} \rightarrow X$ 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 $\phi$ which is strictly decreasing outside $\mathcal{SCR}_d(\phi)$. Such a result generalizes Conley's Fundamental Theorem of Dynamical Systems for the strong chain recurrent set.
Keywords:
recurrent set;
strong chain;
chain recurrent;
lyapunov function
Journal Title: Topology and its Applications
Year Published: 2021
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Journal Title: Topology and its Applications
Year Published: 2021
Link to full text (if available)
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recommendations!