Description

• Title:
  Conley index and homology index braids in singular perturbation problems without uniqueness of solutions
• Creator:
  Carbinatto, Maria C.;
  Rybakowski, Krzysztof P.
• Description:
  We define the concept of a Conley index and a homology index braid class for ordinary differential equations of the form \begin{equation} \dot x= F_1(x), \tag{$E$} \end{equation} where $\mathcal{M}$ is a $C^2$-manifold and $F_1$ is the principal part of a < i> continuous vector field< /i> on $\mathcal{M}$. This allows us to extend our previously obtained results from [M.C. Carbinatto and K.P. Rybakowski, < i> On the suspension isomorphism for index braids in a singular perturbation problem< /i> , Topological Methods in Nonl. Analysis < b> 32< /b> (2008), 199-225] on singularly perturbed systems of ordinary differential equations \begin{equation} \begin{split} \varepsilon\dot y&amp;=f(y,x,\varepsilon),\\ \dot x&amp;=h(y,x,\varepsilon) \end{split} \tag($E_\varepsilon$) \end{equation} on $Y\times \mathcal{M}$, where $Y$ is a finite dimensional Banach space and $\mathcal{M}$ is a $C^2$-manifold, to the case where the vector field in $(E_\varepsilon)$ is continuous, but not necessarily locally Lipschitzian.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2010.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 35, No 1 (March 2010); 1 - 32;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.001/8431
• Subject:
  singular perturbations;
  differential equations on manifolds;
  Conley index;
  (co)homology index braid;
  continuation properties;
  Primary 34D15;
  Secondary 37B30;
  34C40
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.001
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other