Description

• Title:
  Asymtotically stable one-dimensional compact minimal sets
• Creator:
  Athanassopoulos, Konstantin
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2007.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 30, No 2 (December 2007); 397 - 406;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2007.035/8860
• Subject:
  Continuous flow;
  asymptotically stable;
  minimal set;
  isolated invariant set;
  Primary 37B25;
  37B35;
  Secondary 54H20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2007.035
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other