2026-04-17T17:46:19Zhttps://recercat.cat/oai/request

oai:recercat.cat:10459.1/4674152025-09-15T18:29:56Zcom_2072_3622col_2072_479130

00925njm 22002777a 4500 dc García, I. A. (Isaac A.) author Giné, Jaume author Rodero, Ana Livia author 2025-02-02 We are interested in bound the maximum number of small amplitude limit cycles that an analytic planar vector field can have bifurcating from any monodromic singularity as well as its stability and hyperbolic nature. We do not use the Poincaré map approach to this problem. Instead, we propose an algorithmic procedure to construct, under some assumptions, a Dulac function in a neighborhood (may be punctured) of the singularity. This approach is based on the existence of a real analytic invariant curve passing through the singularity which allows us to overcome the usual difficulty seeking for the candidates to be a Dulac function. We finally apply our results to a degenerate polynomial monodromic family. This work is supported by the Agencia Estatal de Investigación grant number PID2020-113758GB-I00; by an AGAUR (Agència de Gestió d'Ajuts Universitaris i de Recerca) grant number 2021SGR-01618; and by the São Paulo Research Foundation (FAPESP), Brasil, Process Numbers 2021/12630-5 and 2023/05686-0. Dulac functions Lyapunov functions Center Dulac functions and monodromic singularities