Local cyclicity in low degree planar piecewise polynomial vector fields

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Author(s):	Gouveia, Luiz F. S. ^{[1, 2]} ; Torregrosa, Joan ^{[2, 3]} Total Authors: 2
Affiliation:	^[1] Univ Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto - Brazil ^[2] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193 - Spain ^[3] Ctr Recerca Matemat, Campus Bellaterra, Barcelona 08193 - Spain Total Affiliations: 3
Document type:	Journal article
Source:	NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 60, AUG 2021.
Web of Science Citations:	0
Abstract
In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small amplitude. They are all nested and surrounding one equilibrium point or a sliding segment. We provide lower bounds for the local cyclicity for planar piecewise polynomial systems, M-c(p)(n), with degrees 2, 3, 4, and 5. More concretely, Mc p (2) >= 13, M-c(p) (3) >= 26, M-c(p) (4) >= 40, and M-c(p) (5) >= 58. The computations use parallelization algorithms. (C) 2020 Elsevier Ltd. All rights reserved. (AU)

FAPESP's process:	20/04717-0 - Dynamical systems with symmetries and implicit differential equations
Grantee:	Luiz Fernando da Silva Gouveia
Support Opportunities:	Scholarships in Brazil - Post-Doctoral