Local cyclicity in low degree planar piecewise polynomial vector fields - Gouveia, Luiz F. S. [UNESP] (2021)
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.