Chaotic Dynamics in a Class of Switched Li\'{e}nard/Rayleigh Systems with Relativistic Acceleration

Abstract

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 Li\'{e}nard 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.