## Topological Methods in Nonlinear Analysis

### Asymtotically stable one-dimensional compact minimal sets

Konstantin Athanassopoulos

#### 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 30, Number 2 (2007), 397-406.

Dates
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463150099

Mathematical Reviews number (MathSciNet)
MR2387834

Zentralblatt MATH identifier
1145.37014

#### Citation

Athanassopoulos, Konstantin. Asymtotically stable one-dimensional compact minimal sets. Topol. Methods Nonlinear Anal. 30 (2007), no. 2, 397--406. https://projecteuclid.org/euclid.tmna/1463150099

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