2026-04-18T07:51:01Zhttps://recercat.cat/oai/request

oai:recercat.cat:10459.1/4687522025-10-09T18:38:08Zcom_2072_3622col_2072_479130

Sufficient Conditions to have Global Centers via Branching Theory Giné, Jaume Yang, Xiao Center Global center Polynomial differential systems It has always been challenging to identify global centers in a planar differential system, despite the recent proposal of a new algorithm to determine such centers. In this paper, we present a novel method for establishing sufficient conditions to achieve a global center. This method is based on determining all the branches that pass through the point at infinity. We apply the method to a specific example to demonstrate how it circumvents the traditional blow-up procedure. The first author is partially supported by the Agencia Estatal de Investigación grant number PID2020-113758GB-I00 and an AGAUR grant number 2021SGR-01618. 2025 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://doi.org/10.1007/s12346-025-01320-z 1575-5460 https://hdl.handle.net/10459.1/468752 http://hdl.handle.net/10459.1/468752 eng 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 CONTINU Reproducció del document publicat a https://doi.org/10.1007/s12346-025-01320-z Qualitative Theory of Dynamical Systems, 2025, vol. 24, 161 cc-by (c) Jaume Giné, Xiao Yang, 2025 Attribution 4.0 International info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ Birkhäuser Verlag