Abstract
It is proved that an asymptotically stable, $1$-dimensional, compact minimal set $A$ of a continuous flow on a locally compact, metric space $X$ is a periodic orbit, if $X$ is locally connected at every point of $A$. So, if the intrinsic topology of the region of attraction of an isolated, $1$-dimensional, compact minimal set $A$ of a continuous flow on a locally compact, metric space is locally connected at every point of $A$, then $A$ is a periodic orbit.
Citation
Konstantin Athanassopoulos. "Asymtotically stable one-dimensional compact minimal sets." Topol. Methods Nonlinear Anal. 30 (2) 397 - 406, 2007.
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