Reversible nilpotent centers with cubic nonlinearities
A real analytic differential system having a center at the origin of coordinates after a linear change of variables and a rescaling of the time can be written in one of the following three forms: (Formula presented.) called a linear type center, (Formula presented.) called a nilpotent center, and (F...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:315711 |
| Acceso en línea: | https://ddd.uab.cat/record/315711 https://dx.doi.org/urn:doi:10.1007/s12215-025-01256-y |
| Access Level: | acceso abierto |
| Palabra clave: | Cubic polynomials differential systems Reversible centers Nilpotent centers |
| Sumario: | A real analytic differential system having a center at the origin of coordinates after a linear change of variables and a rescaling of the time can be written in one of the following three forms: (Formula presented.) called a linear type center, (Formula presented.) called a nilpotent center, and (Formula presented.) called a degenerate center, where X2(x,y) and Y2(x,y) are real analytic functions without constant and linear terms, defined in a neighborhood of the origin. While there are many papers dedicated to study phase portraits of different classes of linear type centers, few papers studied the phase portraits of the nilpotent and degenerate centers. Here we classify the global phase portraits in the Poincaré disc of reversible nilpotent centers with cubic nonlinearities. |
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