Softcover ISBN:  9781470472191 
Product Code:  GSM/228.S 
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AMS Member Price:  $68.00 
eBook ISBN:  9781470472184 
Product Code:  GSM/228.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470472191 
eBook: ISBN:  9781470472184 
Product Code:  GSM/228.S.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $136.00 $102.00 
Softcover ISBN:  9781470472191 
Product Code:  GSM/228.S 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
eBook ISBN:  9781470472184 
Product Code:  GSM/228.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470472191 
eBook ISBN:  9781470472184 
Product Code:  GSM/228.S.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $136.00 $102.00 

Book DetailsGraduate Studies in MathematicsVolume: 228; 2022; 460 ppMSC: Primary 37; Secondary 28; 11; 68
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 nonshift 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, squarefree shifts, density shifts, \(\mathcal{B}\)free shifts, BratteliVershik 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.
ReadershipGraduate students and researchers interested in symbolic dynamics and coding theory.

Table of Contents

Chapters

First examples and general properties of subshifts

Topological dynamics

Subshifts of positive entropy

Subshifts of zero entropy

Further minimal Cantor systems

Methods from ergodic theory

Automata and linguistic complexity

Miscellaneous background topics

Solutions to exercises


Additional Material

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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 nonshift 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, squarefree shifts, density shifts, \(\mathcal{B}\)free shifts, BratteliVershik 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.
Graduate students and researchers interested in symbolic dynamics and coding theory.

Chapters

First examples and general properties of subshifts

Topological dynamics

Subshifts of positive entropy

Subshifts of zero entropy

Further minimal Cantor systems

Methods from ergodic theory

Automata and linguistic complexity

Miscellaneous background topics

Solutions to exercises