The Generalized Recurrent Set, Explosions and Lyapunov Functions
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-019-09788-5
Abstract: We consider explosions in the generalized recurrent set for homeomorphisms on a compact metric space. We provide multiple examples to show that such explosions can occur, in contrast to the case for the chain recurrent… read more here.
Keywords: recurrent set; set explosions; generalized recurrent; explosions lyapunov ... See more keywords
A Conley-type Lyapunov function for the strong chain recurrent set
Sign Up to like & getrecommendations! Published in 2021 at "Topology and its Applications"
DOI: 10.1016/j.topol.2021.107768
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 $\mathcal{SCR}_d(\phi)$.… read more here.
Keywords: recurrent set; strong chain; chain recurrent; lyapunov function ... See more keywords