We study the Nonlinear Shrodinger Equation describing a countable system of hyperbolic oscillators. The criterion of arizing of blow up phenomenon for solutions of Cauchy problem is obtained. The symplectic space of the considered Hamiltonian system is extended such that every solution is continued across the blow up point. The invariant measures of a Hamiltonian flow on the extended phase space are studied. The properties of Koopman unitary presentation of Hamiltonian flow and its self-adjoint generator are described.