  We analyze by a renormalization method, the dynamics of a particle in a
infinite square-well potential driven by an external monochromatic field. This
method set up for Hamiltonian systems with two degrees of freedom allows us to
analyze precisely the stability of the trajectories of the particle as a
function of the amplitude $\epsilon$ of the external field. We compute
numerical values of $\epsilon$ for which the motion of the particle with
frequency $\omega$ is broken and a transition to a chaotic behavior occurs. We
obtain the critical function $\epsilon_c(\omega)$ associated with this system
as a function of the parameters such as the frequency of the field and the
width of the potential.
