Limit cycles of continuous piecewise differential systems formed by linear and quadratic isochronous centers I
First, we study the planar continuous piecewise differential systems separated by the straight line x = 0 formed by a linear isochronous center in x > 0 and an isochronous quadratic center in x < 0. We prove that these piecewise differential systems cannot have crossing periodic orbits, and co...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:257103 |
| Acceso en línea: | https://ddd.uab.cat/record/257103 https://dx.doi.org/urn:doi:10.1142/S0218127422500031 |
| Access Level: | acceso abierto |
| Palabra clave: | Limit cycles Isochronous quadratic centers Continuous piecewise linear differential systems First integrals |
| Sumario: | First, we study the planar continuous piecewise differential systems separated by the straight line x = 0 formed by a linear isochronous center in x > 0 and an isochronous quadratic center in x < 0. We prove that these piecewise differential systems cannot have crossing periodic orbits, and consequently they do not have crossing limit cycles. Second, we study the crossing periodic orbits and limit cycles of the planar continuous piecewise differential systems separated by the straight line x = 0 having in x > 0 the general quadratic isochronous center x =-y + x2-y2, x = x(1 + 2y) after an affine transformation, and in x < 0 an arbitrary quadratic isochronous center. For these kind of continuous piecewise differential systems the maximum number of crossing limit cycles is one, and there are examples having one crossing limit cycles. In short for these families of continuous piecewise differential systems we have solved the extension of the 16th Hilbert problem. |
|---|