Description

• Tytuł:
  Influence of a small perturbation on Poincaré-Andronov operators with not well defined topological degree
• Twórca:
  Makarenkov, Oleg
• Opis:
  Let ${\mathcal P}_\varepsilon\in C^0({\mathbb R}^n,{\mathbb R}^n)$ be the Poincaré-Andronov operator over period $T> 0$ of $T$-periodically perturbed autonomous system $\dot x=f(x)+\varepsilon g(t,x,\varepsilon)$, where $\varepsilon> 0$ is small. Assuming that for $\varepsilon=0$ this system has a $T$-periodic limit cycle $x_0$ we evaluate the topological degree $d(I-{\mathcal P}_\varepsilon,U)$ of $I-{\mathcal P}_\varepsilon$ on an open bounded set $U$ whose boundary $\partial U$ contains $x_0([0,T])$ and ${\mathcal P}_0(v)\not=v$ for any $v\in \partial U\setminus x_0([0,T])$. We give an explicit formula connecting $d(I-{\mathcal P}_\varepsilon,U)$ with the topological indices of zeros of the associated Malkin's bifurcation function. The goal of the paper is to prove the Mawhin's conjecture claiming that $d(I-{\mathcal P}_\varepsilon,U)$ can be any integer in spite of the fact that the measure of the set of fixed points of ${\mathcal P}_0$ on $\partial U$ is zero.
• Dostępność obiektu:
  free access
• Prawa:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Data:
  2008.09.01
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  English
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 32, No 1 (September 2008); 165 - 175;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2008.043/8809
• Temat i słowa kluczowe:
  Topological degree;
  perturbed Poincaré-Andronov map;
  zero measure singularities;
  Primary 54C40;
  14E20;
  Secondary 46E25;
  20C20
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2008.043
• Dostawca danych:
  Akademicka Platforma Czasopism
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