Finite-time Lyapunov exponents for products of random transformations

Details Finite-time Lyapunov exponents for products of random transformations Finite-time Lyapunov exponents for products of random transformations

2003-03-26

arxiv.org/abs/nlin/0303060v1

J. Stat. Phys. 112 (2003) 193-218

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

It is shown how continuous products of random transformations constrained by a generic group structure can be studied by using Iwasawa's decomposition into ``angular'', ``diagonal'' and ``shear'' degrees of freedom. In the case of a Gaussian process a set of variables, adapted to the Iwasawa decomposition and still having a Gaussian distribution, is introduced and used to compute the statistics of the finite-time Lyapunov spectrum of the process. The variables also allow to show the exponential freezing of the ``shear'' degrees of freedom, which contain information about the Lyapunov eigenvectors.

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