Darboux Integrable System with a Triple Point and Pseudo-Abelian Integrals

Affiliation auteursAffiliation ok
TitreDarboux Integrable System with a Triple Point and Pseudo-Abelian Integrals
Type de publicationJournal Article
Year of Publication2020
AuteursBraghtha A
JournalJOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
Volume26
Pagination761-774
Date PublishedOCT
Type of ArticleArticle
ISSN1079-2724
Mots-clésAbelian integrals, Darboux integrability, Limit cycles
Résumé

We study pseudo-Abelian integrals associated with polynomial perturbations of Darboux integrable system with a triple point. Under some assumptions, we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of the corresponding pseudo-Abelian integrals is bounded uniformly for nearby Darboux integrable foliations.
DOI10.1007/s10883-020-09477-3