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arXiv · 0904.1286

From Lyapunov modes to the exponents for hard disk systems

Tony Chung·Daniel Truant·Gary P. Morriss
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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 $ε$ for the transverse and LP modes where $ε$ 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.

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Tony Chung, Daniel Truant, Gary P. Morriss. 2009-04-08. From Lyapunov modes to the exponents for hard disk systems. https://doi.org/10.1103/physreve.81.066208

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