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The Resource Substitutions in dynamics, arithmetics, and combinatorics, N. Pytheas Fogg ; editors, V. Berthé ... [et al.]

Substitutions in dynamics, arithmetics, and combinatorics, N. Pytheas Fogg ; editors, V. Berthé ... [et al.]

Creator
Contributor
Summary
A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems
Language
eng
Work
Publication
Extent
xvii, 402 p.
Contents
  • Basic notions on substitutions / Valerie Berthe and Anne Siegel
  • Substitutions, arithmetic and finite automata / Christian Mauduit
  • Automatic sequences and transcendence / Valerie Berthe
  • Substitutions and partitions of the set of positive integrers / J.-I. Tamura
  • Substitutions and symbolic dynamical systems / Sebastien Ferenczi
  • Sturmian sequences / P. Arnoux
  • Spectral theory and geometric representation of substitutions / Anne Siegel
  • Diophantine approximations, substitutions, and fractals / S. Ito
  • Infinite words generated by invertible substitutions / Z.-Y. Wen
  • Polynomial dynamical systems associated with substitutions / J. Peyriere
  • Piecewise linear transformations of the unit interval and Cantor sets / M. Mori
  • Some open problems / P. Arnoux and Valerie Berthe
  • Undecomposable matrices in dimension 3 / J. Rivat
Isbn
9783540441410
Instance
Label
Substitutions in dynamics, arithmetics, and combinatorics
Title
Substitutions in dynamics, arithmetics, and combinatorics
Statement of responsibility
N. Pytheas Fogg ; editors, V. Berthé ... [et al.]
Creator
Contributor
Subject
Language
eng
Summary
A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Pytheas Fogg, N
Illustrations
illustrations
Index
index present
LC call number
  • QA3
  • QA267
LC item number
  • .L28 no. 1794
  • .P98 2002
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1957-
http://library.link/vocab/relatedWorkOrContributorName
Berthé, V.
Series statement
Lecture notes in mathematics,
Series volume
1794
http://library.link/vocab/subjectName
  • Rewriting systems (Computer science)
  • Combinatorial analysis
  • Computational complexity
  • Réécriture, Systèmes de (Informatique)
  • Analyse combinatoire
  • Complexité de calcul (Informatique)
  • TEORIA DOS NÚMEROS (ÄLGEBRA)
  • Substitutie
  • Rekenkunde
  • Combinatieleer
  • Dynamische systemen
  • Kombinatorische Analysis
  • Berechnungskomplexität
  • Symbolische Dynamik
  • Iteration
  • Kombinatorik
  • Substitution
  • Dynamisches System
  • Reduktionssystem
  • Combinatorial analysis
  • Computational complexity
  • Rewriting systems (Computer science)
Label
Substitutions in dynamics, arithmetics, and combinatorics, N. Pytheas Fogg ; editors, V. Berthé ... [et al.]
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. [377]-397) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Basic notions on substitutions / Valerie Berthe and Anne Siegel -- Substitutions, arithmetic and finite automata / Christian Mauduit -- Automatic sequences and transcendence / Valerie Berthe -- Substitutions and partitions of the set of positive integrers / J.-I. Tamura -- Substitutions and symbolic dynamical systems / Sebastien Ferenczi -- Sturmian sequences / P. Arnoux -- Spectral theory and geometric representation of substitutions / Anne Siegel -- Diophantine approximations, substitutions, and fractals / S. Ito -- Infinite words generated by invertible substitutions / Z.-Y. Wen -- Polynomial dynamical systems associated with substitutions / J. Peyriere -- Piecewise linear transformations of the unit interval and Cantor sets / M. Mori -- Some open problems / P. Arnoux and Valerie Berthe -- Undecomposable matrices in dimension 3 / J. Rivat
Dimensions
24 cm.
Extent
xvii, 402 p.
Isbn
9783540441410
Isbn Type
(pbk. : acid-free paper)
Lccn
2002030325
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
ill.
System control number
  • (OCoLC)50323126
  • (OCoLC)ocm50323126
Label
Substitutions in dynamics, arithmetics, and combinatorics, N. Pytheas Fogg ; editors, V. Berthé ... [et al.]
Publication
Bibliography note
Includes bibliographical references (p. [377]-397) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Basic notions on substitutions / Valerie Berthe and Anne Siegel -- Substitutions, arithmetic and finite automata / Christian Mauduit -- Automatic sequences and transcendence / Valerie Berthe -- Substitutions and partitions of the set of positive integrers / J.-I. Tamura -- Substitutions and symbolic dynamical systems / Sebastien Ferenczi -- Sturmian sequences / P. Arnoux -- Spectral theory and geometric representation of substitutions / Anne Siegel -- Diophantine approximations, substitutions, and fractals / S. Ito -- Infinite words generated by invertible substitutions / Z.-Y. Wen -- Polynomial dynamical systems associated with substitutions / J. Peyriere -- Piecewise linear transformations of the unit interval and Cantor sets / M. Mori -- Some open problems / P. Arnoux and Valerie Berthe -- Undecomposable matrices in dimension 3 / J. Rivat
Dimensions
24 cm.
Extent
xvii, 402 p.
Isbn
9783540441410
Isbn Type
(pbk. : acid-free paper)
Lccn
2002030325
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
ill.
System control number
  • (OCoLC)50323126
  • (OCoLC)ocm50323126

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