Ray dynamics in waveguide media exhibits chaotic motion. For a finite length of propagation, the large distance asymptotics is not uniform and represents a complicated combination of bunches of rays with different intermediate asymptotics. The origin of the phenomena that we call “chaotic transmission,’’ lies in the nonuniformity of the phase space with sticky domains near the boundary of islands. We demonstrate different fractal properties of ray propagation using underwater acoustics as an example. The phenomenon of the kind of Lévy flights can occur and it can be used as a mechanism of cooling of signals when the width of spatial spectra dispersion is significantly reduced.