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Uniqueness of limit cycles in polynomial systems with algebraic invariants

Published online by Cambridge University Press:  17 April 2009

André Zegeling  and
Robert E. Kooij
André Zegeling
Affiliation:
Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands
Robert E. Kooij
Affiliation:
Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands
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Abstract

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The uniqueness of limit cycles is proved for quadratic systems with an invariant parabola and for cubic systems with four real line invariants. Also a new, simple proof is given of the uniqueness of limit cycles occurring in unfoldings of certain vector fields with codimension two singularities.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 1 , February 1994 , pp. 7 - 20
Copyright
Copyright © Australian Mathematical Society 1994

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