New lower bound for the Hilbert number in piecewise quadratic differential systems

Autor(es)

da Cruz, Leonardo P. C. ^[1] ; Novaes, Douglas D. ^[2] ; Torregrosa, Joan ^[1]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain

^[2] Univ Estadual Campinas, Dept Matemat, Rua Sergio Buarque de Holanda, 651, Cidade Univ, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 266, n. 7, p. 4170-4203, MAR 15 2019.
• Citações Web of Science: 3

Resumo

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-p (n) the extension of the Hilbert number to degree n piecewise polynomial differential systems, then H-p (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. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 16/11471-2 - Órbitas deslizantes em sistemas dinâmicos descontínuos: soluções periódicas, conexões homoclínicas, e modos não lineares de deslize
• Beneficiário: Douglas Duarte Novaes
• Linha de fomento: Auxílio à Pesquisa - Regular