Integrability and a Limit Cycle Solver for A Generalization of Polynomial Liénard Differential Systems

摘要

In this paper, we study the periodic orbits of the second-order differential equation. We find a way of study the integrability liénard systems in the plane. In this article such problem is formulated in the more general framework of Poincarée Bendixson structures, which include Hamiltonian systems as a particular case. We deal with the analyticity of the second integral of any (possibly degenerate) center of an analytic planar differential system. A concrete example as application is given.