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arXiv:1106.0857 [math.DS]AbstractReferencesReviewsResources

On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields

Lubomir Gavrilov

Published 2011-06-04, updated 2012-12-12Version 3

We prove that every heteroclinic saddle loop (a two-saddle cycle) occurring in an analytic finite-parameter family of plane analytic vector fields, may generate no more than a finite number of limit cycles within the family.

Comments: 21 pages, 10 figures, a new section explaining the so called "Petrov trick" in the context of the paper is added. The paper will appear in "Functional Analysis and Its Applications" (2013)
Categories: math.DS
Subjects: 34C07, 37G15, 70K05
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