Renormalization and Central Limit Theorem for Critical Dynamical Systems with Weak External Noise

Details Renormalization and Central Limit Theorem for Critical Dynamical Systems with Weak External Noise Renormalization and Central Limit Theorem for Critical Dynamical Systems with Weak External Noise

2006-11-16

arxiv.org/abs/math/0611514v1

Mathematics

Dynamical Systems

79 pages

Scientific paper

We study of the effect of weak noise on critical one dimensional maps; that is, maps with a renormalization theory. We establish a one dimensional central limit theorem for weak noises and obtain Berry--Esseen estimates for the rate of this convergence. We analyze in detail maps at the accumulation of period doubling and critical circle maps with golden mean rotation number. Using renormalization group methods, we derive scaling relations for several features of the effective noise after long times. We use these scaling relations to show that the central limit theorem for weak noise holds in both examples. We note that, for the results presented here, it is essential that the maps have parabolic behavior. They are false for hyperbolic orbits.

Affiliated with

Also associated with

No associations

Rating

Renormalization and Central Limit Theorem for Critical Dynamical Systems with Weak External Noise 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 Renormalization and Central Limit Theorem for Critical Dynamical Systems with Weak External Noise, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Renormalization and Central Limit Theorem for Critical Dynamical Systems with Weak External Noise will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-338281