174 research outputs found
On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields
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.Comment: 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
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