Universitat de Lleida
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.
Anglès
Nonlinear differential systems; Integrability problem; Degenerate center problem; Matemàtica; Mathematics
Elsevier
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
http://creativecommons.org/licenses/by-nc-nd/4.0/
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