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oai:recercat.cat:10459.1/584122024-12-05T22:04:52Zcom_2072_3622col_2072_479130

00925njm 22002777a 4500 dc Algaba, Antonio author Checa, Isabel author García, Cristóbal author Giné, Jaume author 2016-11-07T14:50:39Z 2018-10-31T23:22:55Z 2016 2016-11-07T14:50:39Z In this paper we study the analytic integrability around the origin inside a family of degenerate centers or perturbations of them. For this family analytic integrability does not imply formal orbital equivalence to a Hamiltonian system. It is shown how difficult is the integrability problem even inside this simple family of degenerate centers or perturbations of them. The first and third authors are 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). The fourth author is partially supported by a MINECO/FEDER Grant Number MTM2014-53703-P and by a AGAUR (Generalitat de Catalunya) Grant Number 2014SGR 1204. http://hdl.handle.net/10459.1/58412 Nonlinear differential systems Integrability problem Degenerate center problem Matemàtica Mathematics Analytic integrability inside a family of degenerate centers