Symbolic dynamics is a rapidly growing area of dynamical systems. Although it originated as a method to study general dynamical systems, it has found significant uses in coding for data storage and transmission as well as in linear algebra. This book is the first general textbook on symbolic dynamics and its applications to coding. Mathematical prerequisites are relatively modest (mainly linear algebra at the undergraduate level) especially for the first half of the book. Topics are carefully developed and motivated with many examples, and there are over 500 exercises to test the reader's understanding. The last chapter contains a survey of more advanced topics, and a comprehensive bibliography is included. This book will serve as an introduction to symbolic dynamics for advanced undergraduate students in mathematics, engineering, and computer science.
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Editorial Reviews
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"The book is well organized, and lucidly written. It is completely rigorous and yet easy to read....There is a wealth of examples illustrating the definitions and theorems. They are very instructive in helping to understand the principles involved in the proofs. There are also many exercises ranging from simple verifications to hard problems. The book is to be recommended both as an introductory textbook and as a standard reference in the field." Petr Kurka, Mathematical Reviews
"The presentation combines the necessary rigor with a lucidity that makes this book a pleasure to read. It is not only an excellent text for an introductory course, but should be well suited for self-study." F.W. Stallmann, Computing Reviews
"The book is a model of organization and clarity, consistent in pace and tone, with very few errata....The book aims to be accessible to engineers and even strong undergraduates, and the mathematical prerequisites are correspondingly modest....I was pleased with it as a the main source for a one-semester graduate course, supplemented with more advanced material....the book is a very fine and broadly accessible introduction to symbolic dynamics and coding." Mike Boyle, Siam Review
"The presentation combines the necessary rigor with a lucidity that makes this book a pleasure to read. It is not only an excellent text for an introductory course, but should be well suited for self-study." F.W. Stallmann, Computing Reviews
"The book is a model of organization and clarity, consistent in pace and tone, with very few errata....The book aims to be accessible to engineers and even strong undergraduates, and the mathematical prerequisites are correspondingly modest....I was pleased with it as a the main source for a one-semester graduate course, supplemented with more advanced material....the book is a very fine and broadly accessible introduction to symbolic dynamics and coding." Mike Boyle, Siam Review
Book Description
Although it originated as a method to study general dynamical systems, symbolic dynamics is useful in coding for data storage and transmission as well as in linear algebra. Requiring only a undergraduate knowledge of linear algebra, this first general textbook includes over 500 exercises.
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2 of 2 people found the following review helpful:
5.0 out of 5 stars
Dense but well-written,
By
This review is from: An Introduction to Symbolic Dynamics and Coding (Paperback)
It is late March as I write this. I have been reading the book since mid-January and have made it to page 77. This is in spite of the fact that I put in about 10 hours a week on it. The bulk of the time is spent learning the language for new concepts. I am pleased with the book in that it does an excellent job of foreshadowing those concepts in the wonderful examples and in the exercises.I would give the advice to do as many of the exercises as possible while continuing to read ahead. If you do this, you will be prepare for what is to come, but you will be less likely to get bogged down. I began this book because I wanted to understand entropy. It looks as if I will be well-prepared for that when I get to the topic in a few more weeks. It is only about 20 or so more pages away.
5.0 out of 5 stars
Great Book,
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This review is from: An Introduction to Symbolic Dynamics and Coding (Paperback)
I bought my first copy of this book several years ago and worked through the first two chapters just for fun. Plenty of good problems that are accessible to undergrads but also challenging. I used the book for an undergrad reading course and it went very well. This year I had to purchase another copy of Lind and Marcus because I lost my first one. I am working with a graduate student reading Kitchen's book and it is not long on detail. Lind and Marcus really helped us out a lot. In future I think I would start with Lind and Marcus though Kitchen's book has a lot to offer, too. They are not the same book in any way.
I don't believe there are any accessible books on symbolic dynamics except this one and thankfully it's really well written. I would recommend it to anyone.
2 of 4 people found the following review helpful:
3.0 out of 5 stars
A good book but alot of work to understand,
By A Customer
This review is from: An Introduction to Symbolic Dynamics and Coding (Paperback)
I used this book in a senior level math course named "Symbolic Dynamics". At the time (and still to this day I believe), this was the ONLY undergraduate text available on this subject. Overall this is a good book, but it IS (as another reviewer put it) somewhat densely written and does follow the path of proposition, theorem, corollary; proposition, theorem, corollary,with some examples spaced between them. The examples overall are OK but not great. More examples would have helped. The questions at the end of each section are also OK but some of them are quite tough. Even though this book was I believe written for senior level undergraduates, it easily serves as a graduate textbook (In fact half of the students in my class were taking the course at a graduate level) and takes alot of time and effort to fully grasp for an average math student. However the subject material itself is somewhat difficult in my opinion (although enjoyable). If you're an honors student then you might have an easier time with this book. I did however enjoy using this book as overall it was well written (and it was the only undergraduate text available!).
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Inside This Book
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First Sentence:
Shift spaces are to symbolic dynamics what shapes like polygons and curves are to geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
irreducible sofic shifts, primitive integral matrix, sliding block code, irreducible shift, eventual factor, golden mean shift, strong shift equivalence, sliding block decoder, same sofic shift, primitive integral matrices, nonnegative integral matrices, symbolic adjacency matrices, ideal class condition, marker automorphisms, strong shift equivalent, resolving presentations, symbolic adjacency matrix, irreducible integral matrix, finite equivalence, context free shift, reducible shifts, amalgamation codes, finitely equivalent, proper subshift, same follower set Key Phrases - Capitalized Phrases (CAPs): (learn more)
Embedding Theorem, Decomposition Theorem, Replacement Theorem, Finite-State Coding Theorem, Lower Entropy Factor Theorem, Masking Lemma, Approximate Eigenvector Algorithm, Marker Lemma, Finite Equivalence Theorem, Subtuple Theorem, Baire Category Theorem, Integrality Condition, Spectral Conjecture, Brouwer Fixed Point Theorem, Inversion Formula, Prove Lemma, Shift Equivalence Problem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Shift spaces are to symbolic dynamics what shapes like polygons and curves are to geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
irreducible sofic shifts, primitive integral matrix, sliding block code, irreducible shift, eventual factor, golden mean shift, strong shift equivalence, sliding block decoder, same sofic shift, primitive integral matrices, nonnegative integral matrices, symbolic adjacency matrices, ideal class condition, marker automorphisms, strong shift equivalent, resolving presentations, symbolic adjacency matrix, irreducible integral matrix, finite equivalence, context free shift, reducible shifts, amalgamation codes, finitely equivalent, proper subshift, same follower set Key Phrases - Capitalized Phrases (CAPs): (learn more)
Embedding Theorem, Decomposition Theorem, Replacement Theorem, Finite-State Coding Theorem, Lower Entropy Factor Theorem, Masking Lemma, Approximate Eigenvector Algorithm, Marker Lemma, Finite Equivalence Theorem, Subtuple Theorem, Baire Category Theorem, Integrality Condition, Spectral Conjecture, Brouwer Fixed Point Theorem, Inversion Formula, Prove Lemma, Shift Equivalence Problem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 53
books:
See all 53 books this book cites
31
books
cite this book:
See all 31 books citing this book
- Symbolic Dynamics and Its Applications (Contemporary Mathematics) by Roy L. Adler on 6 pages
- Ergodic Theory (Cambridge Studies in Advanced Mathematics) by Karl E. Petersen on page 445, Back Matter (1), and Back Matter (2)
- Linear Algebra by Michael Ed. Hill in Back Matter (1), and Back Matter (2)
- The Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin in Back Matter
- The Theory of Bernoulli Shifts (Lectures in Mathematics) by Paul C. Shields in Back Matter
See all 53 books this book cites
- Codes, Systems, and Graphical Models by Brian Marcus on 5 pages
- Dynamics and Randomness (Nonlinear Phenomena and Complex Systems) by Alejandro Maass on page 52, page 94, and page 215
- Implementation and Application of Automata: 7th International Conference, CIAA 2002, Tours, France, July 3-5, 2002, Revised Papers (Lecture Notes in Computer Science) by Jean-Marc Champarnaud on page 202, and page 227
- Random Walks and Geometry: Proceedings of a Workshop at the Erwin Schrodinger Institute, Vienna, June 18-July 13, 2001 (De Gruyter Proceedings in Mathematics) by Vadim A. Kaimanovich on page 107, and page 419
- Topics in Dynamics and Ergodic Theory (London Mathematical Society Lecture Note Series) by Sergey Bezuglyi on page 187, and page 223
See all 31 books citing this book
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