On rigorous stability results for low-dimensional KAM surfaces

The stability of invariant (KAM) surfaces for nonintegrable dynamical systems with few degrees of freedom, as a nonlinearity parameter is increased, is considered. A rigorous method, which allows one to construct explicitly such surfaces, is discussed. A byproduct of this method allows one to give lower bounds on breakdown thresholds and applications to the standard map and to a two wave hamiltonian system yield results that agree within 60% with the numerical expectations