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- catalog abstract "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.".
- catalog contributor b12634911.
- catalog contributor b12634912.
- catalog created "c2002.".
- catalog date "2002".
- catalog date "c2002.".
- catalog dateCopyrighted "c2002.".
- catalog description "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.".
- catalog description "Includes bibliographical references (p. [377]-397) and index.".
- catalog description "Preface -- 1. Basic notions on substitutions -- Part I: Arithmetics and combinatorics -- 2. Substitutions, arithmetic and finite automata: an introduction -- 3. Automatic sequences and transcendence -- 4. Substitutions and partitions of the set of positive integers -- Part II: Dynamics of Substitutions -- 5. Substitutions and symbolic dynamical systems -- 6. Sturmian sequences -- 7. Spectral theory and geometric representation of substitutions -- 8. Diophantine approximations, substitutions, and fractals -- Part III: Extensions to free groups and interval transformations -- 9. Infinite words generated by invertible substitutions -- 10. Polynomial dynamical systems associated with substitutions -- 11. Piecewise linear transformations of the unit interval and Cantor sets -- 12. Some open problems -- A. Undecomposable matrices in dimension 3 -- References -- Index.".
- catalog extent "xvii, 402 p. :".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540441417 (pbk. : acid-free paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1794.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1794".
- catalog issued "2002".
- catalog issued "c2002.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 511.3 21".
- catalog subject "Combinatorial analysis.".
- catalog subject "Computational complexity.".
- catalog subject "Computer science.".
- catalog subject "Differentiable dynamical systems.".
- catalog subject "Mathematics.".
- catalog subject "Number theory.".
- catalog subject "QA3 .L28 no. 1794 QA267".
- catalog subject "Rewriting systems (Computer science)".
- catalog subject "Sequences (Mathematics).".
- catalog tableOfContents "Preface -- 1. Basic notions on substitutions -- Part I: Arithmetics and combinatorics -- 2. Substitutions, arithmetic and finite automata: an introduction -- 3. Automatic sequences and transcendence -- 4. Substitutions and partitions of the set of positive integers -- Part II: Dynamics of Substitutions -- 5. Substitutions and symbolic dynamical systems -- 6. Sturmian sequences -- 7. Spectral theory and geometric representation of substitutions -- 8. Diophantine approximations, substitutions, and fractals -- Part III: Extensions to free groups and interval transformations -- 9. Infinite words generated by invertible substitutions -- 10. Polynomial dynamical systems associated with substitutions -- 11. Piecewise linear transformations of the unit interval and Cantor sets -- 12. Some open problems -- A. Undecomposable matrices in dimension 3 -- References -- Index.".
- catalog title "Substitutions in dynamics, arithmetics, and combinatorics / N. Pytheas Fogg ; editors, V. Berthé ... [et al.].".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".