2026-04-14T06:33:49Zhttps://recercat.cat/oai/request

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

2024-12-05T22:04:52Z urn:hdl:10459.1/58412 Analytic integrability inside a family of degenerate centers Algaba, Antonio Checa, Isabel García, Cristóbal Giné, Jaume Nonlinear differential systems Integrability problem Degenerate center problem Matemàtica Mathematics 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. 2024-12-05T22:04:52Z 2024-12-05T22:04:52Z 2016-11-07T14:50:39Z 2018-10-31T23:22:55Z 2016 2016-11-07T14:50:39Z info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion http://hdl.handle.net/10459.1/58412 MINECO/PN2013-2016/MTM2014-56272-C2-2 MINECO/PN2013-2016/MTM2014-53703-P Versió postprint del document publicat a: https://doi.org/10.1016/j.nonrwa.2016.02.003 Nonlinear Analysis-Real World Applications, 2016, vol. 31, p. 288-307 cc-by-nc-nd (c) Elsevier, 2016 info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ Elsevier