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New lower bound for the Hilbert number in piecewise quadratic differential systems
Da Cruz, Leonardo Pereira Costa (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universidade Estadual de Campinas (Brasil). Departamento de Matemática)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date: 2019
Abstract: We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. If we denote by H (n) the extension of the Hilbert number to degree n piecewise polynomial differential systems, then H (2)≥16. As fas as we are concerned, this is the best lower bound for the quadratic class. Moreover, in the studied cases, all limit cycles appear nested bifurcating from a period annulus of a isochronous quadratic center.
Grants: Ministerio de Economía y Competitividad MTM2016-77278-P
Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió acceptada per publicar
Subject: Non-smooth differential system ; Limit cycles in piecewise quadratic differential systems ; First and second order perturbations of isochronous quadratic systems ; Hilbert number for piecewise quadratic differential systems
Published in: Journal of differential equations, Vol. 266, Núm. 7 (March 2019) , p. 4170-4203, ISSN 1090-2732

DOI: 10.1016/j.jde.2018.09.032


Postprint
29 p, 594.7 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2019-05-16, last modified 2022-06-02



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