From Lyapunov modes to the exponents for hard disk systems
Chaotic Dynamics
2015-05-13 v1
Abstract
We demonstrate the preservation of the Lyapunov modes by the underlying tangent space dynamics of hard disks. This result is exact for the zero modes and correct to order for the transverse and LP modes where is linear in the mode number. For sufficiently large mode numbers the dynamics no longer preserves the mode structure. We propose a Gram-Schmidt procedure based on orthogonality with respect to the centre space that determines the values of the Lyapunov exponents for the modes. This assumes a detailed knowledge of the modes, but from that predicts the values of the exponents from the modes. Thus the modes and the exponents contain the same information.
Cite
@article{arxiv.0904.1286,
title = {From Lyapunov modes to the exponents for hard disk systems},
author = {Tony Chung and Daniel Truant and Gary P. Morriss},
journal= {arXiv preprint arXiv:0904.1286},
year = {2015}
}