[en] One studies the dynamical system described by the Hamiltonian H = H₀ + EPSILON V, where H₀ = ¹/₂ p² - cos x, V = - cos (lambda x - Ωt). One encounters this system in a number of problems of practical importance. In addition, the system has intrinsic interest for the theory of adiabaticity and stochasticity. The invariant action J of the unperturbed Hamiltonian H₀ is subject to strong modification or destruction because of the perturbation EPSILON V. Absence of an invariant (i.e., stochasticity) occurs in a phase space region whose size and shape vary with the three parameters EPSILON, lambda, Ω. Previous studies have varied the amplitude of a perturbation (our epsilon); one emphasizes the strong dependences on the space (lambda) and time (Ω) scales of the perturbation. Results show that a perturbation is most effective at causing stochastic motion if its space and time scales are comparable (lambda - 1, Ω - 1) to those in the unperturbed Hamiltonian H₀