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Diffusion Character in Four-Dimensional Volume-Preserving Map

Published online by Cambridge University Press:  12 April 2016

Yi-Sui Sun  and
Yan-Ning Fu
Yi-Sui Sun
Affiliation:
Department of Astronomy, Nanjing University, Nanjing 210093, PR.China
Yan-Ning Fu
Affiliation:
Purple Mountain Observatory, Academia Sinica, Nanjing 210008, P.R.China

Abstract

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Due to the existence of invariant tori, chaotic sea and hyperbolic structures in higher dimensional phase space of a volume-preserving map, the diffusion route of chaotic orbits will be complicated. The velocity of diffusion will be very slow if the orbits are near an invariant torus. In order to realize this complicated diffusion phenomenon, in this paper we study the diffusion characters in the different regions, i.e., chaotic, hyperbolic and invariant tori’s regions. We find that for the three different regions, the diffusion velocities are different. The diffusion velocity in the vicinity of an invariant torus is the slowest one.

Keywords

: Volume-Preserving mapInvariant toriDiffusion
Type
Analytical and Numerical Tools
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 249 - 258
Copyright
Copyright © Kluwer 1999

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