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

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dc.creatorDiaz-Espinosa, Oliver
dc.creatorde la Llave, Rafael
dc.date2006-11-16
dc.date.accessioned2026-07-07T07:33:02Z
dc.date.available2026-07-07T07:33:02Z
dc.descriptionWe 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.
dc.description79 pages
dc.identifierhttps://arxiv.org/abs/math/0611514
dc.identifierhttp://arxiv.org/abs/math/0611514
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119319
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.subject37E20, 60F05, 37C30
dc.titleRenormalization and Central Limit Theorem for Critical Dynamical Systems with Weak External Noise
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