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Existence of periodic orbits of autonomous ordinary differential equations

Published online by Cambridge University Press:  14 November 2011

Russell A. Smith
Russell A. Smith
Affiliation:
Department of Mathematics, University of Durham
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Synopsis

The Poincaré-Bendixson theorem, concerning the existence of periodic orbits of plane autonomous systems, is extended to higher order systems under certain conditions. Under similar conditions, a complementary theorem on the existence of recurrent orbits is also proved. For the feedback control equation, these conditions are reduced to a form which can be easily verified in practice.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 85 , Issue 1-2 , 1980 , pp. 153 - 172
Copyright
Copyright © Royal Society of Edinburgh 1980

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