The Hausdorff dimension spectrum of Renyi-like continued fractions

Autor:	Andrei E. Ghenciu, Sara Munday
Rok vydání:	2021
Předmět:	Pure mathematics Algebra and Number Theory Iterated function system Hausdorff dimension 010102 general mathematics Spectrum (functional analysis) Fraction (mathematics) Conformal map 010103 numerical & computational mathematics 0101 mathematics 01 natural sciences Mathematics
Zdroj:	Journal of Number Theory. 228:359-374
ISSN:	0022-314X
DOI:	10.1016/j.jnt.2021.04.001
Popis:	In this paper, we look at a family of Renyi-like continued fraction expansions and the associated conformal iterated function systems. We show that for every k ≥ 2 , every such associated system has full Hausdorff dimension spectrum. We construct two examples of iterated function systems that do not have full Hausdorff dimension spectrum. One is a subsystem of any given Renyi-like system, while the second consists of similarities.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::f26d1bc0a475c2fe587d8f2db6a0d9d6 https://doi.org/10.1016/j.jnt.2021.04.001 Zobrazit plný text záznamu Full Text from ScienceDirect