Asymtotically stable one-dimensional compact minimal sets
Słowa kluczowe
Continuous flow, asymptotically stable, minimal set, isolated invariant setAbstrakt
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.Pobrania
Opublikowane
2007-12-01
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1.
ATHANASSOPOULOS, Konstantin. Asymtotically stable one-dimensional compact minimal sets. Topological Methods in Nonlinear Analysis [online]. 1 grudzień 2007, T. 30, nr 2, s. 397–406. [udostępniono 22.7.2024].
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