Cyclicity of period annuli and principalization of Bautin ideals

Details Cyclicity of period annuli and principalization of Bautin ideals Cyclicity of period annuli and principalization of Bautin ideals

2007-05-08

arxiv.org/abs/0705.1112v2

Ergodic Theory Dynam. Systems 28 (2008), no. 5, 1497--1507.

Mathematics

Dynamical Systems

14 pages, 1 figure

Scientific paper

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

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