Local cyclicity in low degree planar piecewise polynomial vector fields |
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| Affiliation: | 1. Universidade Estadual Paulista, IBILCE-UNESP, Av. Cristovão Colombo, 2265, 15.054-000, S. J. Rio Preto, SP, Brazil;2. Universitat Autònoma de Barcelona, UAB, Edifici C Facultat de Ciències, 08193 Bellaterra, Barcelona, Spain;3. Universidade Estadual de Campinas, IMECC-UNICAMP, R. Sérgio Buarque de Holanda, 651, 13.083-859, Campinas, SP, Brazil;1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350116, China;2. School of Mathematical Sciences, Peking University, Beijing 100871, China;1. E.P. Superior, Virgen de África 7, 41011 Sevilla, Spain;2. E.T.S. Ingeniería, Camino de los Descubrimientos, 41092 Sevilla, Spain;1. Instituto de Matemática e Estatística, Universidade Federal de Goiás Campus II, Samambaia, 74001-970, Goiânia, GO, Brazil;2. Departamento de Matemática, Universidade Federal de Viçosa, Campus Universitário, 36570-000, Viçosa, MG, Brazil;3. Departamento de Matemática, Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária Zeferino Vaz, 13083-859, Campinas, SP, Brazil |
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| 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, with degrees 2, 3, and 5. More concretely, and The computations use parallelization algorithms. |
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| Keywords: | Piecewise vector field Piecewise center cyclicity Lyapunov quantities |
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