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

Autor(es)

Stadlbauer, Manuel ^[1] ; Zhang, Xuan ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Nonlinearity; v. 34, n. 3, p. 1389-1407, MAR 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 18/15088-4 - Teoremas de limite em sistemas dinâmicos
• Beneficiário: Xuan Zhang
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado