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Limit cycles of a class of polynomial systems

Published online by Cambridge University Press:  14 November 2011

Marc Carbonell  and
Jaume Llibre
Marc Carbonell
Affiliation:
Departament de Matemàtiques i Informàtica, Facultat de Ciències, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain
Jaume Llibre
Affiliation:
Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain
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Synopsis

We study the class of polynomial vector fields of the form = αx — y + Pn(x, y), = x + αy + Qn(x, y), where Pn and Qn are homogeneous polynomials of degree n. If we define the functions f(x, y) = xPn(x, y) + yQn(x, y) and g(x, y) = xQn(x, y)−yPn(x, y), we characterise the number of limit cycles for this class when the function g(αg − f) does not change sign.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 1-2 , 1988 , pp. 187 - 199
Copyright
Copyright © Royal Society of Edinburgh 1988

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