Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T09:58:16.028Z Has data issue: false hasContentIssue false
  • English
  • Français

Liouvillian first integrals for a class of generalized Liénard polynomial differential systems

Part of: Stability theory

Published online by Cambridge University Press:  13 July 2016

Jaume Llibre  and
Clàudia Valls
Jaume Llibre
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain ([email protected])
Clàudia Valls
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal ([email protected])
Get access Rights & Permissions [Opens in a new window]

Extract

We study the existence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form xʹ = y, yʹ = –g(x) – f(x)y, where f(x) = 3Q(x)Qʹ(x)P(x) + Q(x)2 Pʹ(x) and g(x) = Q(x)Qʹ(x)(Q(x)2 P(x)2 – 1) with P,Q ∈ ℂ[x]. This class of generalized Liénard polynomial differential systems has the invariant algebraic curve (y + Q(x)P(x))2 – Q(x)2 = 0 of hyperelliptic type.

Keywords

Darboux polynomialinvariant algebraic curveexponential factorLiouvillian first integralLiénard polynomial differential system

MSC classification

Secondary: 34D30: Structural stability and analogous concepts
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 6 , December 2016 , pp. 1195 - 1210
Copyright
Copyright © Royal Society of Edinburgh 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)