Local cyclicity in low degree planar piecewise polynomial vector fields
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 s...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:236666 |
| Acceso en línea: | https://ddd.uab.cat/record/236666 https://dx.doi.org/urn:doi:10.1016/j.nonrwa.2020.103278 |
| Access Level: | acceso abierto |
| Palabra clave: | Piecewise vector field Piecewise center cyclicity Lyapunov quantities |
| Sumario: | 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, Mc p(n), with degrees 2, 3, 4, and 5. More concretely, Mc p(2) ≥ 13, Mc p(3) ≥ 26, Mc p(4) ≥ 40, and Mc p(5) ≥ 58. The computations use parallelization algorithms. |
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