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oai:recercat.cat:2117/9812025-07-17T05:24:29Zcom_2072_1033col_2072_452950

Geometric tools to determine the hyperbolicity of limit cycles Guillamon Grabolosa, Antoni Sabatini, Marco Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions Differential equations Differentiable dynamical systems hyperbolicity of limit cycles Equacions diferencials ordinàries Sistemes dinàmics diferenciables Classificació AMS::34 Ordinary differential equations::34A General theory Classificació AMS::34 Ordinary differential equations::34C Qualitative theory Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory In this paper we present a new method to study limit cycles’ hyperbolicity. The main tool is the function ? = ([V,W] ^ V )/(V ^W), where V is the vector field under investigation and W a transversal one. Our approach gives a high degree of freedom for choosing operators to study the stability. It is related to the divergence test, but provides more information on the system’s dynamics. We extend some previous results on hyperbolicity and apply our results to get limit cycles’ uniqueness. Li´enard systems and conservative+dissipative systems are considered among the applications. 2005 Article https://hdl.handle.net/2117/981 eng http://creativecommons.org/licenses/by-nc-nd/2.5/es/ Open Access Attribution-NonCommercial-NoDerivs 2.5 Spain 19 application/pdf