Computing center conditions for vector fields with constant angular speed
We investigate the planar analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The conditions for the origin to be a center (in fact, an isochronous center) are obtained. Concretely, we find conditions for the existence of a Cw-commutator of the f...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2003 |
| País: | España |
| Institución: | Universidad de Huelva (UHU) |
| Repositorio: | Arias Montano. Repositorio Institucional de la Universidad de Huelva |
| Idioma: | inglés |
| OAI Identifier: | oai:ariasmontano.uhu.es:10272/25437 |
| Acceso en línea: | https://hdl.handle.net/10272/25437 |
| Access Level: | acceso abierto |
| Palabra clave: | Limit cycles Periodic solutions 1206.02 Ecuaciones Diferenciales |
| Sumario: | We investigate the planar analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The conditions for the origin to be a center (in fact, an isochronous center) are obtained. Concretely, we find conditions for the existence of a Cw-commutator of the field. We cite several subfamilies of centers and obtain the centers of the cuartic polynomial systems and of the families (-y + x(H1 + Hm), x + y(H1 + Hm)1 and (-y + x(H2 + H2n), x + y(H2 + H2n))t, with H i homogeneous polynomial in x,y of degree i. In these cases, the maximum number of limit cycles which can bifurcate from a fine focus is determined. |
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