Periodic solutions of the perturbed symmetric Euler top

Abstract

We study the problem of persistence of $T$-periodic solutions of the celebrated symmetric Euler top when subjected to a small $T$-periodic stimulus. All solutions of the unperturbed system are periodic (of different periods, including continua of equilibria). In the case that the perturbation depends also on the three components of the angular momentum (the unknowns of the system) we provide bifurcation functions whose simple zeros correspond to $T$-periodic solutions of the perturbed system.