Puiseux Integrability of Differential Equations

  1. Demina, Maria V. 1
  2. Giné, Jaume 2
  3. Valls, Claudia 3
  1. 1 Higher School of Economics, National Research University
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    Higher School of Economics, National Research University

    Moscú, Rusia

    ROR https://ror.org/055f7t516

  2. 2 Universitat de Lleida
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    Universitat de Lleida

    Lleida, España

    ROR https://ror.org/050c3cw24

  3. 3 Universidade de Lisboa
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    Universidade de Lisboa

    Lisboa, Portugal

    ROR https://ror.org/01c27hj86

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Revista:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Año de publicación: 2022

Volumen: 21

Número: 2

Tipo: Artículo

DOI: 10.1007/S12346-022-00565-2 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Qualitative theory of dynamical systems

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.

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