Chaotic Dynamics in a Class of Switched Liénard/Rayleigh Systems with Relativistic Acceleration

We consider a class of time-periodic switched systems, which are obtained as a perturbation of a planar autonomous reversible system by a periodic forcing term. The model is motivated by an extension of the classical Liénard and Rayleigh equations due to the presence of a relativistic acceleration. Using recent results from the theory of topological horseshoes, we provide a new result of existence of infinitely many subharmonic solutions, as well as more complex dynamics, as illustrated by some numerical examples.