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
Chain recurrent points of monotone graph maps and CR-Pm property on local dendrites
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2018.1561881
Abstract: ABSTRACT In this paper, the set of chain recurrent points of monotone maps on graphs is investigated. A compact metric space X has the CR-Pm property provided that for each monotone self-mapping f of X,… read more here.
Keywords: recurrent points; chain recurrent; points monotone; property ... See more keywords