Analytically Integrable Centers of Perturbations of Cubic Homogeneous Systems

  1. Algaba, Antonio 1
  2. García, Cristóbal 1
  3. Reyes, Manuel 1
  1. 1 Universidad de Huelva

    Universidad de Huelva

    Huelva, España


Qualitative theory of dynamical systems

ISSN: 1575-5460

Year of publication: 2021

Volume: 20

Issue: 2

Type: Article

DOI: 10.1007/S12346-021-00479-5 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Qualitative theory of dynamical systems


We consider the analytically integrable perturbations of cubic homogeneous differential systems whose origin is an isolated singularity. We prove that are orbitally equivalent to the cubic vector field associated. We also characterize the analytically integrable centers. We apply the results to two families of degenerate vector fields.

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