Birkhoff lower-dimensional tori in Hamiltonian systems

CONSIDER a C~l (l≥3) area-preserving diffeomorphism f: U→R~2, defined in a neighbourhoodU of origin O in a plane and assume that f(O)=O and Df(O) has a pair of pure imaginaryeigenvalues eω≠2πm/n, i. e. origin O is an elliptic fixed point of f. In generic casesone can write f=B+C, where the ristriction of B to each circle p~2+q~2=2τis a rotation