An Introduction to Symbolic Dynamics and Coding 2nd Edition by Douglas Lind, Brian Marcus 9781108901963 1108901964

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• ISBN 10:1108901964 

• ISBN 13:9781108901963

• Author:Douglas Lind, Brian Marcus 

 An Introduction to Symbolic Dynamics and Coding
Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C^*$-algebras. This Second Edition maintains the introductory character of the original 1995 edition as a general textbook on symbolic dynamics and its applications to coding. It is written at an elementary level and aimed at students, well-established researchers, and experts in mathematics, electrical engineering, and computer science. Topics are carefully developed and motivated with many illustrative examples. There are more than 500 exercises to test the reader’s understanding. In addition to a chapter in the First Edition on advanced topics and a comprehensive bibliography, the Second Edition includes a detailed Addendum, with companion bibliography, describing major developments and new research directions since publication of the First Edition.

An Introduction to Symbolic Dynamics and Coding 2nd Table of contents:

CHAPTER 1 SHIFT SPACES
§1.1. Full Shifts
§1.2. Shift Spaces
§1.3. Languages
§1.4. Higher Block Shifts and Higher Power Shifts
§1.5. Sliding Block Codes
§1.6. Convolutional Encoders
CHAPTER 2 SHIFTS OF FINITE TYPE
§2.1. Finite Type Constraints
§2.2. Graphs and Their Shifts
§2.3. Graph Representations of Shifts of Finite Type
§2.4. State Splitting
§2.5. Data Storage and Shifts of Finite Type
CHAPTER 3 SOFIC SHIFTS
§3.1. Presentations of Sofic Shifts
§3.2. Characterizations of Sofic Shifts
§3.3. Minimal Right-Resolving Presentations
§3.4. Constructions and Algorithms
CHAPTER 4 ENTROPY
§4.1. Definition and Basic Properties
§4.2. Perron–Frobenius Theory
§4.3. Computing Entropy
§4.4. Irreducible Components
§4.5. Cyclic Structure
CHAPTER 5 FINITE-STATE CODES
§5.1. Road Colorings and Right-Closing Labelings
§5.2. Finite-State Codes
§5.3. Approximate Eigenvectors
§5.4. Code Construction
§5.5. Sliding Block Decoders
CHAPTER 6 SHIFTS AS DYNAMICAL SYSTEMS
§6.1. Metric Spaces
§6.2. Dynamical Systems
§6.3. Invariants
§6.4. Zeta Functions
§6.5. Markov Partitions
CHAPTER 7 CONJUGACY
§7.1. The Decomposition Theorem
§7.2. Strong Shift Equivalence
§7.3. Shift Equivalence
§7.4. Invariants for Shift Equivalence
§7.5. Shift Equivalence and the Dimension Group
CHAPTER 8 FINITE-TO-ONE CODES AND FINITE EQUIVALENCE
§8.1. Finite-to-One Codes
§8.2. Right-Resolving Codes
§8.3. Finite Equivalence
§8.4. Right-Resolving Finite Equivalence
CHAPTER 9 DEGREES OF CODES AND ALMOST CONJUGACY
§9.1. The Degree of a Finite-to-One Code
§9.2. Almost Invertible Codes
§9.3. Almost Conjugacy
§9.4. Typical Points According to Probability
CHAPTER 10 EMBEDDINGS AND FACTOR CODES
§10.1. The Embedding Theorem
§10.2. The Masking Lemma
§10.3. Lower Entropy Factor Codes
CHAPTER 11 REALIZATION
§11.1. Realization of Entropies
§11.2. Realization of Zeta Functions
§11.3. Pure Subgroups of Dimension Groups
CHAPTER 12 EQUAL ENTROPY FACTORS
§12.1. Right-Closing Factors
§12.2. Eventual Factors of Equal Entropy
§12.3. Ideal Classes
§12.4. Sufficiency of the Ideal Class Condition
CHAPTER 13 GUIDE TO ADVANCED TOPICS
§13.1. More on Shifts of Finite Type and Sofic Shifts
§13.2. Automorphisms of Shifts of Finite Type
§13.3. Symbolic Dynamics and Stationary Processes
§13.4. Symbolic Dynamics and Ergodic Theory
§13.5. Sofic-like Shifts
§13.6. Continuous Flows
§13.7. Minimal Shifts
§13.8. One-Sided Shifts
§13.9. Shifts with a Countable Alphabet
§13.10. Higher Dimensional Shifts
ADDENDUM
§A.1. Classification Problems
§A.2. Factor Codes and Embeddings
§A.3. Symbolic Models for Smooth Systems
§A.4. Realization
§A.5. Automorphism Groups of Shifts
§A.6. Higher Dimensional Shifts
§A.7. Equilibrium States
§A.8. Symbolic Dynamics over Countable Groups
§A.9. Symbolic Representations of Algebraic Actions
BIBLIOGRAPHY
ADDENDUM BIBLIOGRAPHY
NOTATION INDEX
INDEX
 

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