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Cyclicity of period annuli and principalization of Bautin ideals

Published online by Cambridge University Press:  01 October 2008

LUBOMIR GAVRILOV
LUBOMIR GAVRILOV*
Affiliation:
Institut de Mathématiques de Toulouse, UMR 5219, Université Paul-Sabatier (Toulouse III), 31062 Toulouse, Cedex 9, France (email: lubomir.gavrilov@math.ups-tlse.fr)
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Abstract

Let Π be an open period annulus of a plane analytic vector field X0. We prove that the maximal number of limit cycles which bifurcate from Π under a given multi-parameter analytic deformation Xλ of X0 is the same as in an appropriate one-parameter analytic deformation Xλ(ε), provided that this cyclicity is finite. Along the same lines, we also give a bound for the cyclicity of homoclinic saddle loops.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 5 , October 2008 , pp. 1497 - 1507
Copyright
Copyright © 2008 Cambridge University Press

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