Limiting Behavior of Random Continued Fractions

Autor:	Lisa Lorentzen
Rok vydání:	2013
Předmět:	Discrete mathematics Combinatorics Computational Mathematics Iterated function system General Mathematics Probability distribution Fraction (mathematics) Limiting Analysis Mathematics
Zdroj:	Constructive Approximation. 38:171-191
ISSN:	1432-0940 0176-4276
DOI:	10.1007/s00365-013-9198-y
Popis:	Let K(an/bn) be a continued fraction with elements (an,bn) picked randomly and independently from \((\mathbb{C}\setminus\{0\})\times\mathbb{C}\) according to some probability distribution μ. We find sufficient conditions on μ for K(an/bn) to converge with probability 1 or to be restrained with probability 1. More generally, we also consider μ-random sequences {τn} of independent Mobius transformations and find sufficient conditions for \(\{\tau_{1}\circ\tau_{2}\circ\cdots\circ\tau_{n}\}_{n=1}^{\infty}\) to converge or be restrained with probability 1. The analysis is based on an important paper by Furstenberg.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::52066f33bfd7c99e5a40a5b700c25041 https://doi.org/10.1007/s00365-013-9198-y Zobrazit plný text záznamu Plný text ve formátu PDF