Maximally Chaotic Dynamical Systems of Anosov-Kolmogorov and Fundamental Interactions

We give a general review on the application of Ergodic theory to investigation dynamics Yang-Mills gauge fields and gravitational systems, as well its in Monte Carlo method fluid dynamics. In ergodic maximally chaotic dynamical systems (MCDS) can be defined that have nonzero Kolmogorov entropy. The hyperbolic fulfil Anosov C-condition belong MCDS insofar they exponential instability their phase trajectories positive It follows defines rich class span over an open set space all systems. large Anosov-Kolmogorov is realised Riemannian manifolds negative sectional curvatures high-dimensional tori. interest rooted attempts understand relaxation phenomena, foundations statistical mechanics, appearance turbulence dynamics, non-linear field gravitating N-body black hole thermodynamics. Our aim investigate classical- quantum-mechanical properties role fundamental interactions.