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

2011/06/04 by Lubomir Gavrilov, Gavrilov, Lubomir
Biochemistry, Genetics and Molecular Biology · Mathematics · #34C07 #37G15 #70K05 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Lipid metabolism and biosynthesis #math.DS #msc:34C07 #msc:37G15 #msc:70K05

paper · pdf · doi:10.48550/arxiv.1106.0857

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)

openalex publication_date 2011/06/04 · arxiv created 2012/12/12 · arxiv updated 2012/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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