FROM THE NEWTON VERSION OF THE KOLMOGOROV-ARNOL'D-MOSER THEORY TO A WEAKLY DISSIPATIVE VERSION

摘要

In this paper, we present results of the numerical study of statistical macroscopic parameters in dynamics of a test particle (or ensembles of particles) in the potential field of an anti-harmonic oscillator with weakly dissipative perturbation starting from the Bogdanov-Tackens bifurcation. This is the most well-studied example of perturbation of Hamiltonian dynamics in the class of all (smooth) dynamical systems. It is possible to characterize stochastic and regular regimes of the test particle dynamics and also interaction of particles by using methods of statistical mechanics and statistical physics.