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Regular version of the site

Article

Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems

Physics Letters A. 2018. Vol. 382. No. 20. P. 1353-1360.

The general structure of irreducible invariant algebraic curves for a polynomial dynamical system in C^2 is found. Necessary conditions for existence of exponential factors related to an invariant algebraic curve are derived. As a consequence, all the cases when the classical force-free Duffing and Duffing–van der Pol oscillators possess Liouvillian first integrals are obtained. New exact solutions for the force-free Duffing–van der Pol system are constructed.