Noise induced dissipation in Lebesgue-measure preserving maps on $d-$dimensional torus

Details Noise induced dissipation in Lebesgue-measure preserving maps on $d-$dimensional torus Noise induced dissipation in Lebesgue-measure preserving maps on $d-$dimensional torus

2002-09-18

arxiv.org/abs/math/0209231v3

Mathematics

Dynamical Systems

The research is supported in part by the grant from U.S. National Science Foundation, DMS-9971322 and Lech Wolowski

Scientific paper

We consider dissipative systems resulting from the Gaussian and $alpha$-stable noise perturbations of measure-preserving maps on the $d$ dimensional torus. We study the dissipation time scale and its physical implications as the noise level $\vep$ vanishes. We show that nonergodic maps give rise to an $O(1/\vep)$ dissipation time whereas ergodic toral automorphisms, including cat maps and their $d$-dimensional generalizations, have an $O(\ln{(1/\vep)})$ dissipation time with a constant related to the minimal, {\em dimensionally averaged entropy} among the automorphism's irreducible blocks. Our approach reduces the calculation of the dissipation time to a nonlinear, arithmetic optimization problem which is solved asymptotically by means of some fundamental theorems in theories of convexity, Diophantine approximation and arithmetic progression. We show that the same asymptotic can be reproduced by degenerate noises as well as mere coarse-graining. We also discuss the implication of the dissipation time in kinematic dynamo.

Affiliated with

Also associated with

No associations

Rating

Noise induced dissipation in Lebesgue-measure preserving maps on $d-$dimensional torus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Noise induced dissipation in Lebesgue-measure preserving maps on $d-$dimensional torus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Noise induced dissipation in Lebesgue-measure preserving maps on $d-$dimensional torus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-196650