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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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-Doctorate