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On the use of the topological degree theory in broken orbits analysis


Authors: A. V. Pokrovskii and O. A. Rasskazov
Journal: Proc. Amer. Math. Soc. 132 (2004), 567-577
MSC (2000): Primary 58C30; Secondary 47H11
DOI: https://doi.org/10.1090/S0002-9939-03-07036-9
Published electronically: September 5, 2003
MathSciNet review: 2022383
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Abstract: Dynamical systems $f$ in ${\mathbb R}^{d}$ are studied. Let $\mbox{\boldmath $\Omega$ } \subset{\mathbb R}^{d}$ be a bounded open set. We will be interested in those periodic orbits such that at least one of its points lies inside $\mbox{\boldmath$\Omega$ }$ and at least one of its points lies outside $\overline{\mbox{\boldmath$\Omega$ }}$; the orbits with this property are called $\mbox{\boldmath$\Omega$ }$-broken. Information about the structure of the set of $\mbox{\boldmath$\Omega$ }$-broken orbits is suggested; results are formulated in terms of topological degree theory.


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Additional Information

A. V. Pokrovskii
Affiliation: Department of Applied Mathematics, National University of Ireland, University College, Cork, Ireland
Email: a.pokrovskii@ucc.ie

O. A. Rasskazov
Affiliation: Institute for Nonlinear Science, Department of Physics, National University of Ireland, University College, Cork, Ireland
Email: oll@phys.ucc.ie

DOI: https://doi.org/10.1090/S0002-9939-03-07036-9
Keywords: Index sequence, topological degree, periodic orbits
Received by editor(s): July 28, 2002
Published electronically: September 5, 2003
Additional Notes: This research was partially supported by the Enterprise Ireland, Grant SC/2000/138
Communicated by: Michael Handel
Article copyright: © Copyright 2003 American Mathematical Society

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