2026-04-18T04:12:56Zhttps://recercat.cat/oai/request

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

urn:hdl:10459.1/467415 Dulac functions and monodromic singularities García, I. A. (Isaac A.) Giné, Jaume Rodero, Ana Livia Dulac functions Lyapunov functions Center 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. 2025-02-02 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/ PID2020-113758GB-I00/ES/ANALISIS CUALITATIVO, INTEGRABILIDAD Y BIFURCACIONES EN SISTEMAS DINAMICOS CONTINUOS Versió postprint del document publicat a https://doi.org/10.1016/j.jmaa.2025.129309 Journal of Mathematical Analysis and Applications, 2025, vol. 547, núm. 2, 129309 cc-by-nc-nd (c) Elsevier, 2025 info:eu-repo/semantics/embargoedAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ Elsevier