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Pàgina inicial > Articles > Articles publicats > Unfolding of saddle-nodes and their Dulac time |
Data: | 2016 |
Resum: | In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we give a uniform asymptotic expansion of the trajectories arriving at the node. Uniformity is with respect to all parameters including the unfolding parameter bringing the node to a saddle-node and a parameter belonging to a space of functions. In the second part, we apply this first result for proving a regularity result (Theorem B) on the Dulac time (time of Dulac map) of an unfolding of a saddle-node. This result is a building block in the study of bifurcations of critical periods in a neighborhood of a polycycle. Finally, we apply Theorem A and Theorem B to the study of critical periods of the Loud family of quadratic centers and we prove that no bifurcation occurs for certain values of the parameters (Theorem C). |
Ajuts: | Ministerio de Economía y Competitividad MTM2011-26674-C02-01 Ministerio de Economía y Competitividad MTM-2008-03437 |
Nota: | Altres ajuts: UNAB10-4E-378, co-funded by ERDF "A way to build Europe" and by the French ANR-11-BS01-0009 STAAVF. |
Drets: | Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Period function ; Unfolding of a saddle-node ; Asymptotic expansions |
Publicat a: | Journal of differential equations, Vol. 261, issue 11 (Dec. 2016) , p. 6411-6436, ISSN 1090-2732 |
Post-print 21 p, 2.2 MB |