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

Abstract

Altres ajuts: ICREA Academia, FEDER-UNAB10-4E378 and PTDC/MAT/117106/2010

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