Measure-wise disjoint Rauzy fractals with the same incidence matrix

The properties of the intersection of Rauzy fractals associated with substitutions having the same incidence matrix have been studied by several authors. Different techniques have been introduced and used for this purpose, one of them is the balanced pair algorithm. In the present paper we explore t...

Full description

Saved in:
Bibliographic Details
Published inMonatshefte für Mathematik Vol. 194; no. 4; pp. 857 - 871
Main Authors Scheicher, Klaus, Sirvent, Víctor F., Surer, Paul
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 01.04.2021
Springer Nature B.V
Subjects
Algorithms
Fractals
Mathematics
Mathematics and Statistics
Substitution dynamical systems
Rauzy fractals
37B10
11B85
28A80
Balanced pair algorithm
Pisot conjecture
Online AccessGet full text
ISSN0026-9255
1436-5081
DOI10.1007/s00605-021-01515-x

Cover

More Information
Summary:The properties of the intersection of Rauzy fractals associated with substitutions having the same incidence matrix have been studied by several authors. Different techniques have been introduced and used for this purpose, one of them is the balanced pair algorithm. In the present paper we explore the actual limitations of this algorithm. We show that the balanced pair algorithm is defined and terminates only when the intersection of the Rauzy fractals have non-empty interior and when this condition fails it cannot be used.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-021-01515-x