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exponential factor

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Liouvillian first integrals for a class of generalized Liénard polynomial differential systems
Part of
- Stability theory
Jaume Llibre, Clàudia Valls
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 146 / Issue 6 / December 2016

Published online by Cambridge University Press:

13 July 2016, pp. 1195-1210

Print publication:

December 2016
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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.