Result: On the lengths of basic intervals in beta expansions
Title:
On the lengths of basic intervals in beta expansions
Authors:
Source:
Nonlinearity (Bristol. Print). 25(5):1329-1343
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 18 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Théorie des opérateurs, Operator theory, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Croissance, Growth, Crecimiento, Expansion, Expansión, Nombre réel, Real number, Número real, Physique mathématique, Mathematical physics, Física matemática, 47A10, Développement mathématique, Mathematical expansion
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
LAMFA-CNRS UMR 6140, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens, France
School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074 Wuhan, China
School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074 Wuhan, China
ISSN:
0951-7715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.25877421
Database:
PASCAL Archive
Further Information
Let β > 1 be a real number and let (∈1 (x, β), ∈2 (x, β),...) be the digit sequence in the β-expansion of a point x ∈ (0, 1]. This note is concerned with the length of the nth order basic interval containing x, denoted by In(x), which consists of those points y ∈ (0, 1] such that ∈j(y, β) = ∈j(x, β) for all 1 ≤ j ≤ n. We establish a relationship between the length of In(x) and the β-expansion of 1, which enables us to obtain the exact value of the length of In(x). As an application, we prove that the growth of the length of In(x) is multifractal and that the multifractal spectrum depends on β.