2026-04-14T05:33:00Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4116822024-10-31T00:15:44Zcom_2072_98col_2072_378192

00925njm 22002777a 4500 dc Mardesic, Pavao author Marín Pérez, David author Saavedra, M. author Villadelprat Yagüe, Jordi author 2016 Altres ajuts: UNAB10-4E-378, co-funded by ERDF "A way to build Europe" and by the French ANR-11-BS01-0009 STAAVF. 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). Period function Unfolding of a saddle-node Asymptotic expansions Unfolding of saddle-nodes and their Dulac time