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Ergodity of the Motions in the Dynamical Systems with Two Degrees of Freedom

Published online by Cambridge University Press:  12 April 2016

T.A. Agekian ,
A.A. Mylläri  and
V.V. Orlov
T.A. Agekian
Affiliation:
Astronomical Observatory, St. Petersburg State Univ. Bibliotechnaya pl. 2, 198904, St. Petersburg Petrodvorets, Russia
A.A. Mylläri
Affiliation:
Dept. of Applied Maths and Cybernetics, Russia

Abstract

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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

Type
Part II Ergodic and Stochastic Motion
Information
International Astronomical Union Colloquium , Volume 132: Instability, Chaos and Predictability in Celestial Mechanics and Stellar Dynamics , 1993 , pp. 93 - 96
Copyright
Copyright © Nova Science Publishers 1993

References

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