Giorgilli A., Lazutkin V.F. Some remarks on the problem of ergodicity of the Standard Map (267K, LATeX) ABSTRACT. We consider the problem of removing the islands of stability in the phase space of the standard map by means of tuning the parameter. A possible construction which gives a classification of periodic chains of islands in terms of a symbolic dynamics and predicts the values of the parameters for which the island with a given symbolic code exists is suggested and discussed.