Mixed Simultaneous Cyclicity for Piecewise Smooth Vector Fields Defined on an Invariant Sphere
In this work we consider the class of partially integrable 3-dimensional piecewise smooth vector fields Y=(X+,X-) with separation set Σ={(x,y,z)∈R3:z=0} and first integral H(x,y,z)=x2+y2+z2 that leaves invariant any sphere centered at the origin, Sρ2={(x,y,z)∈R3:x2+y2+z2=ρ2}. We denote this class by...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:uabarcelona_::2a7a2d1e79f1772d55e7d023c34df266 |
| Acceso en línea: | https://ddd.uab.cat/record/328867 https://dx.doi.org/urn:doi:10.1007/s10884-026-10507-0 |
| Access Level: | acceso abierto |
| Palabra clave: | Piecewise smooth vector fields on an invariant sphere Integrability Mixed simultaneous cyclicity |
| Sumario: | In this work we consider the class of partially integrable 3-dimensional piecewise smooth vector fields Y=(X+,X-) with separation set Σ={(x,y,z)∈R3:z=0} and first integral H(x,y,z)=x2+y2+z2 that leaves invariant any sphere centered at the origin, Sρ2={(x,y,z)∈R3:x2+y2+z2=ρ2}. We denote this class by X and by Xn when X± are polynomial vector fields of degree n. Our main goal is to study piecewise smooth vector fields in the class X1 presenting three periodic annuli on the invariant sphere S12 proving that there exists a mixed simultaneous configuration with at least five limit cycles bifurcating simultaneously of them, considering polynomial perturbations inside the class X2. |
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