Description

• Title:
  The suspension isomorphism for homology index braids
• Creator:
  Carbinatto, Maria C.;
  Rybakowski, Krzysztof P.
• Description:
  Let $X$ be a metric space, $\pi$ be a local semiflow on $X$, $k\in\mathbb N$, $E$ be a $k$-dimensional normed space and $\widetilde\pi$ be the semiflow generated by the equation $\dot y=Ly$, where $L\co E\to E$ is a linear map whose all eigenvalues have positive real parts. We show in this paper that for every admissible isolated $\pi$-invariant set $S$ there is a well-defined isomorphism of degree $-k$ from the homology categorial Conley-Morse index of $(\pi\times\widetilde\pi,S\times\{0\})$ to the homology categorial Conley-Morse index of $(\pi,S)$ such that the family of these isomorphisms commutes with homology index sequences. In particular, given a partially ordered Morse decomposition $(M_i)_{i\in P}$ of $S$ there is an isomorphism of degree $-k$ from the homology index braid of $(M_i\times\{0\})_{i\in P}$ to the homology index braid of $(M_i)_{i\in P}$, so $C$-connection matrices of $(M_i\times\{0\})_{i\in P}$ are just $C$-connection matrices of $(M_i)_{i\in P}$ shifted by $k$ to the right.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2006.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 28, No 2 (December 2006); 199 - 233;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2006.028/8875
• Subject:
  Conley index;
  homology index braid;
  suspension isomorphism;
  connection matrix;
  Primary 37B30;
  Secondary 37C70;
  55N10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2006.028
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other