Analytical integrability problem for perturbations of cubic Kolmogorov systems
We solve, by using normal forms, the analytic integrability problem for differential systems in the plane whose first homogeneous component is a cubic Kolmogorov system being the origin an isolated singularity. As an application, we give the analytically integrable systems of a class of systems x&am...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| 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:10272/25428 |
| Acceso en línea: | https://hdl.handle.net/10272/25428 |
| Access Level: | acceso abierto |
| Palabra clave: | Quadratic and cubic systems Kolmogorov systems Integrability Linearization Inverse Integrating Factors 1206.02 Ecuaciones Diferenciales |
| Sumario: | We solve, by using normal forms, the analytic integrability problem for differential systems in the plane whose first homogeneous component is a cubic Kolmogorov system being the origin an isolated singularity. As an application, we give the analytically integrable systems of a class of systems x' = x(P2 + P3); y' = y(Q2 +Q3); being Pi;Qi homogeneous polynomials of degree i. We also prove that for any n>=3, there are analytically integrable perturbations of x' = xPn; y' = yQn which are not orbital equivalent to its first homogeneous component. |
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