Opis

• Tytuł:
  Index 1 fixed points of orientation reversing planar homeomorphisms
• Twórca:
  Salazar, José M.;
  Ruiz del Portal, Francisco Romero
• Opis:
  Let \(U \subset {\mathbb R}^2\) be an open subset, \(f\colon U \rightarrow f(U) \subset {\mathbb R}^2\) be an orientation reversing homeomorphism and let \(0 \in U\) be an isolated, as a~periodic orbit, fixed point. The main theorem of this paper says that if the fixed point indices \(i_{{\mathbb R}^2}(f,0)=i_{{\mathbb R}^2}(f^2,0)=1\) then there exists an orientation preserving dissipative homeomorphism $\varphi\colon {\mathbb R}^2 \rightarrow {\mathbb R}^2$ such that \(f^2=\varphi\) in a~small neighbourhood of \(0\) and \(\{0\}\) is a~global attractor for \(\varphi\). As a corollary we have that for orientation reversing planar homeomorphisms a~fixed point, which is an isolated fixed point for \(f^2\), is asymptotically stable if and only if it is stable. We also present an application to periodic differential equations with symmetries where orientation reversing homeomorphisms appear naturally.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Data:
  2015.09.01
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 46, No 1 (September 2015); 223 - 246;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.044/7207
• Temat i słowa kluczowe:
  Fixed point index;
  Conley index;
  orientation reversing homeomorphisms;
  attractors;
  stability;
  37B30;
  37C25
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.044
• Dostawca danych:
  Akademicka Platforma Czasopism
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