Invariant tori with prescribed frequency for nearly integrable hamiltonian systems

In this paper, we consider real analytic nearly integrable hamiltonian systems under Bruno non-degeneracy condition, and prove that if the rank of the Jacobian of the n-dimensional frequency vectors with respect to action variables is n − 1, then there exists a one-parameter analytic family of invariant tori, whose frequencies are the small dilation of a prescribed Diophantine frequency vector.