Geometry of the common dynamics of flipped Pisot substitutions

Bernd Sing, V Sirvent

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this article we study the common dynamics of two different Pisot substitutions sigma(1) and sigma(2) having the same incidence matrix. This common dynamics arises in the study of the adic systems associated with the substitutions sigma(1) and sigma(2). Since the adic systems considered here have geometric realizations given by solutions to graph-directed iterated function systems, we actually study topological and measure-theoretic properties of the solution of those iterated function systems which describe the common dynamics.
Original languageEnglish
Pages (from-to)431-448
Number of pages18
JournalMonatshefte für Mathematik
Volume155
Issue number3-4
DOIs
Publication statusPublished - 2008

Fingerprint

Substitution
Iterated Function System
Incidence Matrix
Directed Graph

Keywords

  • Model sets
  • Adic systems
  • Finite automata
  • Substitutions
  • Rauzy fractals

Cite this

Geometry of the common dynamics of flipped Pisot substitutions. / Sing, Bernd; Sirvent, V.

In: Monatshefte für Mathematik, Vol. 155, No. 3-4, 2008, p. 431-448.

Research output: Contribution to journalArticle

Sing, Bernd ; Sirvent, V. / Geometry of the common dynamics of flipped Pisot substitutions. In: Monatshefte für Mathematik. 2008 ; Vol. 155, No. 3-4. pp. 431-448.
@article{36c8359cc22c4ad5ab81c668bb2b423e,
title = "Geometry of the common dynamics of flipped Pisot substitutions",
abstract = "In this article we study the common dynamics of two different Pisot substitutions sigma(1) and sigma(2) having the same incidence matrix. This common dynamics arises in the study of the adic systems associated with the substitutions sigma(1) and sigma(2). Since the adic systems considered here have geometric realizations given by solutions to graph-directed iterated function systems, we actually study topological and measure-theoretic properties of the solution of those iterated function systems which describe the common dynamics.",
keywords = "Model sets, Adic systems, Finite automata, Substitutions, Rauzy fractals",
author = "Bernd Sing and V Sirvent",
year = "2008",
doi = "10.1007/s00605-008-0004-z",
language = "English",
volume = "155",
pages = "431--448",
journal = "Monatshefte fur Mathematik",
issn = "0026-9255",
publisher = "Springer Wien",
number = "3-4",

}

TY - JOUR

T1 - Geometry of the common dynamics of flipped Pisot substitutions

AU - Sing, Bernd

AU - Sirvent, V

PY - 2008

Y1 - 2008

N2 - In this article we study the common dynamics of two different Pisot substitutions sigma(1) and sigma(2) having the same incidence matrix. This common dynamics arises in the study of the adic systems associated with the substitutions sigma(1) and sigma(2). Since the adic systems considered here have geometric realizations given by solutions to graph-directed iterated function systems, we actually study topological and measure-theoretic properties of the solution of those iterated function systems which describe the common dynamics.

AB - In this article we study the common dynamics of two different Pisot substitutions sigma(1) and sigma(2) having the same incidence matrix. This common dynamics arises in the study of the adic systems associated with the substitutions sigma(1) and sigma(2). Since the adic systems considered here have geometric realizations given by solutions to graph-directed iterated function systems, we actually study topological and measure-theoretic properties of the solution of those iterated function systems which describe the common dynamics.

KW - Model sets

KW - Adic systems

KW - Finite automata

KW - Substitutions

KW - Rauzy fractals

UR - http://www.scopus.com/inward/record.url?scp=56749160181&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/s00605-008-0004-z

U2 - 10.1007/s00605-008-0004-z

DO - 10.1007/s00605-008-0004-z

M3 - Article

VL - 155

SP - 431

EP - 448

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 3-4

ER -