Kolmogorov tori in certain nonintegrable systems, not containing small parameters (Q1112637)

It is proved that in systems of special form there exists a Kolmogorov set and it fills the entire phase space, except some set of finite measure. Estimates are given for the relative measure of the Kolmogorov set and for the deformation quantities of the Kolmogorov tori. The obtained results are applied in the problems on the plane oscillations of a pendulum with a vibrating point of support and of a satellite moving along an elliptic orbit, and also in a restricted problem on the rotation of a symmetric heavy body with a fixed point.