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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).
Idioma original | Anglès |
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Revista | Journal of Differential Equations |
DOIs | |
Estat de la publicació | En premsa - 2016 |
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Variedades complejas, dinámica holomorfa y singularidades
Marin Perez, D. (PI), Mattei, J. F. (Investigador/a) & Nicolau Reig, M. (Investigador/a)
1/01/12 → 31/12/15
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