On the metric theory of particle transport in a random velocity field (the problem of turbulent diffusion). Part II

Summary

The concept of the metric theory of particle transfer in a random field of velocities the problem of turbulent diffusion is the result of a suitable connection of a certain computational theoretical model of the endomorphism of Lebesgue's space L and the concept of the action of the field of velocities on the particle in its abstract form. The metric theory of this phenomenon is part of the general metric theory of dynamic systems, i.e. the ergodic theory. The adjective “suitable” means that we are introducing certain relations between the said concepts. The essence of these concepts is in that we require that the relations, describing the nature of the field-particle interaction, be a realistic counterpart to the appropriate endomorphism T of space L. This endomorphism is closely associated with Kolmogorov's automorphism and with the automorphism with a positive enthropy. We are pointing out the close relation between the T-representation, the equations of motion of the particle in a random field of velocities, the canonic transformations and the fundamental model of stochasticity of Hamiltonian systems.