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Published online by Cambridge University Press: 12 April 2016
We study a process of stochastization of the motions in an example of the Henon-Heiles model. We propose a new method to study this process a method of the field of directions of motion in the meridional plane. A numerical integration of the equation for the derivative of this field ∂f/∂n to the normal to a trajectory has been made. We denote the points in which ∂f/∂n → ± ∞, and derive the contours of orbit and folds of directions. The growth of ergodity is connected with the increase of a number and an area of the folds. May be, a successive doubling of a number of folds takes place that results in a chaos. In the transition region we found a complex periodical orbit. The interpretation of this fact may be made as an example of cantori. A transition region has very small sizes about 10−4