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Analytical Integrability of Perturbations of Quadratic Systems

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Abstract

We consider analytic perturbations of quadratic homogeneous differential systems having an isolated singularity at the origin. We characterize the systems with an analytic first integral at the origin. We apply the results to two families of degenerate vector fields.

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Acknowledgements

The authors are partially supported by a MINECO/FEDER grant number MTM2014-56272-C2-2 and by the Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658, FQM-276).

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Authors and Affiliations

  1. Department of Integrated Sciences, Center of Advanced Studies in Physics Mathematics and Computation Huelva University, 21071, Huelva, Spain

    Antonio Algaba, Cristóbal García & Manuel Reyes

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  1. Antonio Algaba
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  2. Cristóbal García
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  3. Manuel Reyes
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Correspondence to Manuel Reyes.

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Algaba, A., García, C. & Reyes, M. Analytical Integrability of Perturbations of Quadratic Systems. Mediterr. J. Math. 18, 8 (2021). https://doi.org/10.1007/s00009-020-01647-8

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  • DOI: https://doi.org/10.1007/s00009-020-01647-8

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