Center cyclicity for some nilpotent singularities including the Z2-equivariant class
This work concerns with polynomial families of real planar vector fields having a monodromic nilpotent singularity. The families considered are those for which the centers are characterized by the existence of a formal inverse integrating factor vanishing at the singularity with a leading term of mi...
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/72482 |
| Acceso en línea: | https://doi.org/10.1142/S0219199720500534 http://hdl.handle.net/10459.1/72482 |
| Access Level: | acceso abierto |
| Palabra clave: | Cyclicity Limit cycle Center |
| Sumario: | This work concerns with polynomial families of real planar vector fields having a monodromic nilpotent singularity. The families considered are those for which the centers are characterized by the existence of a formal inverse integrating factor vanishing at the singularity with a leading term of minimum $(1,n)$-quasihomogeneous weighted degree, being $n$ the Andreev number of the singularity. These families strictly include the case $n=2$ and also the $\mathbb{Z}_2$-equivariant families. In some cases for such families we solve, under additional assumptions, the local Hilbert 16th problem giving global bounds on the maximum number of limit cycles that can bifurcate from the singularity under perturbations within the family. Several examples are given. |
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