Local cyclicity in low degree planar piecewise polynomial vector fields

Autor(es)

Gouveia, Luiz F. S. ^{[1, 2]} ; Torregrosa, Joan ^{[2, 3]}

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 60, AUG 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 20/04717-0 - Sistemas dinâmicos com simetrias e equações diferenciais implícitas
• Beneficiário: Luiz Fernando da Silva Gouveia
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado