Asymtotically stable one-dimensional compact minimal sets
Keywords
Continuous flow, asymptotically stable, minimal set, isolated invariant setAbstract
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.Downloads
Published
2007-12-01
How to Cite
1.
ATHANASSOPOULOS, Konstantin. Asymtotically stable one-dimensional compact minimal sets. Topological Methods in Nonlinear Analysis. Online. 1 December 2007. Vol. 30, no. 2, pp. 397 - 406. [Accessed 23 April 2024].
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