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Effective Lyapunov Numbers and Correlation Dimensions in a 3-D Hamiltonian System

Published online by Cambridge University Press:  12 April 2016

K. Tsiganis ,
A. Anastasiadis  and
H. Varvoglis
K. Tsiganis
Affiliation:
Section of Astrophysics, Astronomy & Mechanics, Department of Physics, Aristotle University of Thessaloniki, 54006 Thessaloniki, GREECE
A. Anastasiadis
Affiliation:
Section of Astrophysics, Astronomy & Mechanics, Department of Physics, Aristotle University of Thessaloniki, 54006 Thessaloniki, GREECE
H. Varvoglis
Affiliation:
Section of Astrophysics, Astronomy & Mechanics, Department of Physics, Aristotle University of Thessaloniki, 54006 Thessaloniki, GREECE

Extract

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Transport in Hamiltonian systems, in the case of strong perturbation, can be modeled as a diffusion process, with the diffusion coefficient being constant and related to the maximal Lyapunov number (Konishi 1989). In this respect the relation found by Lecar et al. (1992) between the escape time of asteroids, TE, and the Lyapunov time, TL, can be easilly recovered (Varvoglis & Anastasiadis 1996). However, for moderate perturbations, chaotic trajectories may have a peculiar evolution, owing to stickiness effects or migration to adjacent stochastic regions. As a result, the function χ(t), which measures the exponential divergence of nearby trajectories, changes behaviour within different time intervals. Therefore, trajectories may be divided into segments, i = 1,..., n, each one being assigned an “Effective” Lyapunov Number (ELN), λi = χ(ti).

Type
Extended Abstracts
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 447 - 448
Copyright
Copyright © Kluwer 1999

References

Contopoulos, G. and Barbanis, B., 1989, A& A 222, 329 Google Scholar
Gaspard, P. andBaras, F., 1995, Phys. Rev. E 51, 6, 5332 CrossRefGoogle Scholar
Isliker, H., 1994, Ph.D. Thesis, ETH: No 10495, Swiss Federal Institute of Technology, ZürichGoogle Scholar
Konishi, T., 1989, Prog. Theor. Phys. Suppl. 98, 19 Google Scholar
Milani, A. and Nobili, A.M., 1992, Nature 357, 569 CrossRefGoogle Scholar
Takens, F., 1981, Lecture Notes in Mathematics, vol. 898 (Springer, New York, 1981)Google Scholar
Varvoglis, H. and Anastasiadis, A., 1996, AJ 111, 1718 Google Scholar
Zaslavsky, G., (1994), Phys. D 76, 110 Google Scholar