Chaotic dynamics in a periodically perturbed Liénard system

Abstract

We prove the existence of infinitely many periodic solutions, as well as the presence of chaotic dynamics, for a periodically perturbed planar Liénard system of the form $\dot{x} = y - F(x) + p(\omega t),\; \dot{y} = - g(x)$. We consider the case in which the perturbing term is not necessarily small. Such a result is achieved by a topological method, that is by proving the presence of a horseshoe structure.