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This paper consider the functional mechanics as one of modern approaches to aproblem of the correspondence between classical mechanics and the statisticalphysics. Deviations from classical trajectories are calculated and evolution ofthe moments of distribution function is constructed. The relation between thereceived results and absence of paradox of Poincare-Zermelo in the functionalmechanics is discussed. Destruction of periodicity of movement in thefunctional mechanics is shown and decrement of attenuation for classicalinvariants of movement on a trajectory of functional mechanical averages iscalculated.

The functional mechanics: evolution of the moments of distribution function and the Poincare recurrence theorem