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 | References | Similar Articles | Additional Information

Abstract: Dynamical systems in are studied. Let be a bounded open set. We will be interested in those periodic orbits such that at least one of its points lies inside and at least one of its points lies outside ; the orbits with this property are called -broken. Information about the structure of the set of -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