The investigations of the color dynamics of Yang-Mills fields was carried out in refs. [7, 8]. It was found by Matinyan and Savidy (1981) that for homogeneous Yang-Mills fields the color dynamics is described by simple Hamiltonian models with few degrees of freedom. The first analysis of these models was done in numerical experiments [7]. There it was shown for the first time that the dynamics of these models has positive Lyapunov exponent and that it is chaotic. In this sense ref. [7] closed the long debates about complete integrability of classical Yang-Mills equations. For the models with Higgs [8] it was shown that due to degeneracy the Kolmogorov-Arnold-Moser theorem cannot be applied and the classical chaos exists for arbitrary small energy (small nonlinearity).