Rigorous and numerical determination of rotational invariant curves for the standard map

Rigorous and numerical results for the determination of rotational invariant curves are presented. The methods are applied to the particular case of the Chirikov standard mapping. In the first part, the KAM theory is developed and the construction of the golden mean curve is performed in detail. In the second part, the numerical method developed by J. Greene on the determination of the stochasticity threshold is explained. An appendix on the computation of the diophantine constant for the golden sectio is added.