  We consider the classical problem of the continuation of periodic orbits
surviving to the breaking of invariant lower dimensional resonant tori in
nearly integrable Hamiltonian systems. In particular we extend our previous
results (presented in CNSNS, 61:198-224, 2018) for full dimensional resonant
tori to lower dimensional ones. We develop a constructive normal form scheme
that allows to identify and approximate the periodic orbits which continue to
exist after the breaking of the resonant torus. A specific feature of our
algorithm consists in the possibility of dealing with degenerate periodic
orbits. Besides, under suitable hypothesis on the spectrum of the approximate
periodic orbit, we obtain information on the linear stability of the periodic
orbits feasible of continuation. A pedagogical example involving few degrees of
freedom, but connected to the classical topic of discrete solitons in
dNLS-lattices, is also provided.
