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...

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Detalles Bibliográficos
Autores: Algaba Durán, Antonio, García García, Cristóbal, Matemático, Reyes Columé, Manuel
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
Descripción
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.