On the Poincaré problem and Liouvillian integrability of quadratic Liénard differential equations

Author:

Demina Maria V.,Valls Claudia

Abstract

AbstractWe present the complete classification of irreducible invariant algebraic curves of quadratic Liénard differential equations. We prove that these equations have irreducible invariant algebraic curves of unbounded degrees, in contrast with what is wrongly claimed in the literature. In addition, we classify all the quadratic Liénard differential equations that admit a Liouvillian first integral.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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