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.

中文翻译：

---

周期扰动的Liénard系统中的混沌动力学

对于形式为$ \ dot {x} = y-F（x）+ p（\ omega t）的周期扰动的平面Liénard系统，我们证明了存在无限多个周期解以及混沌动力学的存在， \; \ dot {y} =-g（x）$。我们考虑扰动项不一定很小的情况。通过拓扑方法，即通过证明存在马蹄形结构来获得这种结果。