On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients

Stadlbauer, Manuel; Zhang, Xuan

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients

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Author(s):	Stadlbauer, Manuel ^[1] ; Zhang, Xuan ^[2] Total Authors: 2
Affiliation:	^[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941909 Rio De Janeiro, RJ - Brazil ^[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil Total Affiliations: 2
Document type:	Journal article
Source:	Nonlinearity; v. 34, n. 3, p. 1389-1407, MAR 2021.
Web of Science Citations:	0
Abstract
We establish a law of the iterated logarithm (LIL) for the set of real numbers whose nth partial quotient is bigger than alpha(n), where (alpha(n)) is a sequence such that n-ary sumation 1/alpha(n) is finite. This set is shown to have Hausdorff dimension 1/2 in many cases and the measure in LIL is absolutely continuous to the Hausdorff measure. The result is obtained as an application of a strong invariance principle for unbounded observables on the limit set of a sequential iterated function system. (AU)

FAPESP's process:	18/15088-4 - Limit theorems in dynamical systems
Grantee:	Xuan Zhang
Support Opportunities:	Scholarships in Brazil - Post-Doctoral

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