Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems

Invariant tori for analytic nearly integrable Hamiltonian systems are constructed under rather weak sufficient conditions being even necessary in the case of maximal invariant tori. All small devisors are controlled by a general approximation function the properties of which correspond to the Bruno condition in analytic problems near a singular point. The admitted size of the perturbations is numerically determined in numerically given systems.