Dissipation time and decay of correlations

Details Dissipation time and decay of correlations Dissipation time and decay of correlations

2003-11-13

arxiv.org/abs/math/0311209v3

Nonlinearity 17 (4) 1481-1508 (2004)

Mathematics

Dynamical Systems

26 Pages, LaTex. Submitted to Nonlinearity

Scientific paper

10.1088/0951-7715/17/4/018

We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and its associated propagators: spectral properties, local expansivity, and global mixing properties. We show that the dissipation is slow for a general class of non-weakly-mixing maps; on the opposite, it is fast for a large class of exponentially mixing systems which include uniformly expanding maps and Anosov diffeomorphisms.

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