Opis

• Tytuł:
  On the suspension isomorphism for index braids in a singular perturbation problem
• Twórca:
  Carbinatto, Maria C.;
  Rybakowski, Krzysztof P.
• Opis:
  We consider the singularly perturbed system of ordinary differential equations $$ \aligned \varepsilon\dot y&=f(y,x,\varepsilon), \\ \dot x&=h(y,x,\varepsilon) \endaligned \leqno(E_\varepsilon) $$ on $Y\times \Cal{M}$, where $Y$ is a finite dimensional normed space and $\Cal{M}$ is a smooth manifold. We assume that there is a reduced manifold of $(E_\varepsilon)$ given by the graph of a function $\phi\co \Cal{M}\to Y$ and satisfying an appropriate hyperbolicity assumption with unstable dimension $k\in{\mathbb N}_0$. We prove that every Morse decomposition $(M_p)_{p\in P}$ of a compact isolated invariant set $S_0$ of the reduced equation $$ \dot x=h(\phi(x),x,0) $$ gives rises, for $\varepsilon> 0$ small, to a Morse decomposition $(M_{p,\varepsilon})_{p\in P}$ of an isolated invariant set $S_\varepsilon$ of $(E_\varepsilon)$ such that $(S_\varepsilon,(M_{p,\varepsilon})_{p\in P})$ is close to $(\{0\}\times S_0,(\{0\}\times M_p)_{p\in P})$ and the (co)homology index braid of $(S_\varepsilon,(M_{p,\varepsilon})_{p\in P})$ is isomorphic to the (co)homology index braid of $(S_0,(M_{p})_{p\in P})$ shifted by $k$ to the left.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Data:
  2008.12.01
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 32, No 2 (December 2008); 199 - 225;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2008.046/8780
• Temat i słowa kluczowe:
  Singular perturbations;
  differential equations on manifolds;
  Conley index;
  (co)homology index braid;
  continuation properties;
  Primary 34D15;
  Secondary 37B30;
  34C40
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2008.046
• Dostawca danych:
  Akademicka Platforma Czasopism
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