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

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Author(s):	da Cruz, Leonardo P. C. ^[1] ; Novaes, Douglas D. ^[2] ; Torregrosa, Joan ^[1] Total Authors: 3
Affiliation:	^[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 Total Affiliations: 2
Document type:	Journal article
Source:	Journal of Differential Equations; v. 266, n. 7, p. 4170-4203, MAR 15 2019.
Web of Science Citations:	3
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-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)

FAPESP's process:	16/11471-2 - Sliding motion in discontinuous dynamical systems: periodic solutions, homoclinic connections, and nonlinear sliding modes
Grantee:	Douglas Duarte Novaes
Support Opportunities:	Regular Research Grants