Description

• Title:
  Nonautonomous Conley index theory. Continuation of Morse-decompositions
• Creator:
  Jänig, Axel
• Description:
  In previous works the author established a nonautonomous Conley index based on the interplay between a nonautonomous evolution operator and its skew-product formulation. In this paper, the treatment of attractor-repeller decomposition is refined. The more general concept of partially ordered Morse-decompositions is used. It is shown that, in the nonautonomous setting, these Morse-decompositions persist under small perturbations. Furthermore, a continuation property for these Morse decompositions is established. Roughly speaking, the index of every Morse-set and every connecting homomorphism continue as the nonautonomous problem, depending continuously on a parameter, changes.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.03.02
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 53, No 1 (March 2019); 79 - 96;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.040/16934 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2018.040/16935
• Subject:
  Nonautonomous differential equations;
  attractor-repeller decompositions;
  Morse-Conley index theory;
  partially orderd Morse-decompositions;
  homology index braid;
  continuation property;
  nonautonomous Conley index;
  homology Conley index;
  Primary;
  37B30;
  37B55;
  Secondary;
  34C99;
  35B08;
  35B40;
  35B99
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.040
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other