Substitutions In Dynamics Arithmetics And Combinatorics
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Substitutions In Dynamics Arithmetics And Combinatorics
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Author : N. Pytheas Fogg
language : en
Publisher: Springer
Release Date : 2003-10-24
Substitutions In Dynamics Arithmetics And Combinatorics written by N. Pytheas Fogg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-24 with Mathematics categories.
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.
Combinatorics On Words
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Author : Anna Frid
language : en
Publisher: Springer Nature
Release Date : 2023-05-30
Combinatorics On Words written by Anna Frid and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-30 with Mathematics categories.
This book constitutes the refereed proceedings of the 14th International Conference on Combinatorics on Words, WORDS 2023, held in Umeå, Sweden, during June 12–16, 2023. The 19 contributed papers presented in this book were carefully reviewed and selected from 28 submissions. In addition, the volume also contains 3 invited papers. WORDS is the main conference series devoted to combinatorics on words. This area is connected to several topics from computer science and mathematics, including string algorithms, automated proofs, discrete dynamics, number theory and, of course, classical combinatorics
Algebraic And Topological Dynamics
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Author : S. F. Koli︠a︡da
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Algebraic And Topological Dynamics written by S. F. Koli︠a︡da and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects. Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statisticalproperties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.
Topological And Ergodic Theory Of Symbolic Dynamics
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Author : Henk Bruin
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-20
Topological And Ergodic Theory Of Symbolic Dynamics written by Henk Bruin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-20 with Mathematics categories.
Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.
Substitution Dynamical Systems Spectral Analysis
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Author : Martine Queffélec
language : en
Publisher: Springer
Release Date : 2010-01-30
Substitution Dynamical Systems Spectral Analysis written by Martine Queffélec and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-30 with Mathematics categories.
This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.
Combinatorics Automata And Number Theory
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Author : Valérie Berthé
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-12
Combinatorics Automata And Number Theory written by Valérie Berthé and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-12 with Mathematics categories.
This collaborative volume presents trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory. Presenting several important tools and concepts, the authors also reveal some of the exciting and important relationships that exist between these different fields. Topics include numeration systems, word complexity function, morphic words, Rauzy tilings and substitutive dynamical systems, Bratelli diagrams, frequencies and ergodicity, Diophantine approximation and transcendence, asymptotic properties of digital functions, decidability issues for D0L systems, matrix products and joint spectral radius. Topics are presented in a way that links them to the three main themes, but also extends them to dynamical systems and ergodic theory, fractals, tilings and spectral properties of matrices. Graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, fractals, tilings and stringology will find much of interest in this book.
Substitution And Tiling Dynamics Introduction To Self Inducing Structures
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Author : Shigeki Akiyama
language : en
Publisher: Springer Nature
Release Date : 2020-12-05
Substitution And Tiling Dynamics Introduction To Self Inducing Structures written by Shigeki Akiyama and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-05 with Mathematics categories.
This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings.
Combinatorics On Words
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Author : Robert Mercaş
language : en
Publisher: Springer Nature
Release Date : 2019-09-02
Combinatorics On Words written by Robert Mercaş and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-02 with Mathematics categories.
This book constitutes the refereed proceedings of the 12th International Conference on Combinatorics on Words, WORDS 2019, held in Loughborough, UK, in September 2019. The 21 revised full papers presented in this book together with 5 invited talks were carefully reviewed and selected from 34 submissions. WORDS is the main conference series devoted to the mathematical theory of words. In particular, the combinatorial, algebraic and algorithmic aspects of words are emphasized. Motivations may also come from other domains such as theoretical computer science, bioinformatics, digital geometry, symbolic dynamics, numeration systems, text processing, number theory, etc.
Combinatorics On Words
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Author : Juhani Karhumäki
language : en
Publisher: Springer
Release Date : 2013-08-15
Combinatorics On Words written by Juhani Karhumäki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-15 with Computers categories.
This book constitutes the refereed proceedings of the 9th International Conference on Combinatorics on Words, WORDS 2013, held in Turku, Finland, in September 2013 under the auspices of the EATCS. The 20 revised full papers presented were carefully reviewed and selected from 43 initial submissions. The central topic of the conference is combinatorics on words (i.e. the study of finite and infinite sequence of symbols) from varying points of view, including their combinatorial, algebraic and algorithmic aspects, as well as their applications.
Mathematics Of Aperiodic Order
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Author : Johannes Kellendonk
language : en
Publisher: Birkhäuser
Release Date : 2015-06-05
Mathematics Of Aperiodic Order written by Johannes Kellendonk and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-05 with Mathematics categories.
What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.