On the use of the topological degree theory in broken orbits analysis
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- by A. V. Pokrovskii and O. A. Rasskazov PDF
- Proc. Amer. Math. Soc. 132 (2004), 567-577 Request permission
Abstract:
Dynamical systems $f$ in ${\mathbb R}^{d}$ are studied. Let $\mathbf {\Omega } \subset \mathbb {R}^{d}$ be a bounded open set. We will be interested in those periodic orbits such that at least one of its points lies inside $\mathbf {\Omega }$ and at least one of its points lies outside $\mathbf {\overline {\Omega }}$; the orbits with this property are called $\mathbf {\Omega }$-broken. Information about the structure of the set of $\mathbf {\Omega }$-broken orbits is suggested; results are formulated in terms of topological degree theory.References
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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
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2022383