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Invariant algebraic curves and conditions for a centre

Published online by Cambridge University Press:  14 November 2011

C. J. Christopher
C. J. Christopher
Affiliation:
Department of Mathematics, University of Wales, Aberystwyth, Dyfed, Wales SY23 3BZ, U.K.
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Abstract

Conditions for the existence of a centre in two-dimensional systems are considered along the lines of Darboux. We show how these methods can be used in the search for maximal numbers of bifurcating limit cycles. We also extend the method to include more degenerate cases such as are encountered in less generic systems. These lead to new classes of integrals. In particular, the Kukles system is considered, and new centre conditions for this system are obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 6 , 1994 , pp. 1209 - 1229
Copyright
Copyright © Royal Society of Edinburgh 1994

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