Estimation of the density particle fluxes in the weakly dissipative Kolmogorov-Arnol’d-Mozer theory

New calculated data on estimation of the density of particle fluxes are presented. These particles move freely in a surrounding medium during the constant transit time and are then rescattered under the potential force field weakly perturbed by generalized viscosity forces. An anharmonic potential on a phase straight line is taken as a potential, and the generalized viscosity force corresponds to a small viscosity coefficient affinely dependent on the phase coordinate. The word “small’ here means that the order of the generalized viscosity forces is less than two. The particle fluxes correspond to the periodic motion of particles, asymptotically stable (unstable) states (“in” and “out” states) as t → (−) + ∞ that have basins of attraction (repulsion) with a positive measure.