
We study the influence of small perturbations of symplectic
structure and of Hamiltonian function on the behavior of a completely
integrable Hamiltonian system whose phase space is stratified by the
Lagrangian invariant tori. It is shown that, in quite general case,
near certain family of these tori there appears a domain which contains a
Cantor set of coisotropic invariant tori of the perturbed system. The
relative measure of such a set tends to one when the magnitude of the
perturbations decreases to zero.
