Renormalization and central limit theorem for critical dynamical systems with weak external noise
Year: 2007
Type: article
Abstract: We study the effect of weak noise on criticalone-dimensional maps; that is, maps with a renormalizationtheory. We establish a one-dimensional central limit theorem for weak noise and obtain Berry--Esseen estimates for the rate ofthis convergence. We analyze in detail maps at the accumulation of period doublingand critical circle maps with golden mean rotation number.Using renormalization group methods,we derive scaling relations for several features of the effective noiseafter long periods. We use these scaling relations toshow 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 arefalse for hyperbolic orbits.
Source: Journal of Modern Dynamics
Authors: Oliver Díaz-Espinosa, Rafael de la Llave
Institution: The University of Texas at Austin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W1974632243