Puiseux Integrability of Differential Equations

• Demina, Maria V. ^[3] ; Giné, Jaume ^[1] ; Valls, Claudia ^[2]
  1. [1] Universitat de Lleida

     Universitat de Lleida

     Lérida, España

     
  2. [2] Universidade de Lisboa

     Universidade de Lisboa

     Socorro, Portugal

     
  3. [3] HSE University

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
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• Resumen

  • In this work we study polynomial differential systems in the plane and define a new type of integrability that we call Puiseux integrability. As its name indicates, the Puiseux integrability is based on finding and studying the structure of Puiseux series that are solutions of a first order ordinary differential equation related to the original differential system. The necessary and sufficient conditions to have such integrability are given. These conditions are used to solve the integrability problem for quintic Liénard differential systems with a cubic damping function.