PLENTY OF ELLIPTIC ISLANDS FOR THE STANDARD FAMILY OF AREA-PRESERVINGMAPS

For the Standard Map, a well-known family of conservative diffeomorphi sms on the torus, we construct large basic sets which fill in the toru s as the parameter runs to infinity. Then we prove that, for a residua l set of large parameters, these basic sets are accumulated by ellipti c periodic islands. We also show that there exists a k0 > 0 and a dens e set of parameters in [k0,infinity) for which the standard map exhibi ts homoclinic tangencies.