An Introduction to Symbolic Dynamics and Coding

Author: Douglas Lind,Brian Marcus

Publisher: Cambridge University Press

ISBN: 9780521559003

Category: Mathematics

Page: 495

View: 3689

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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An Introduction to Symbolic Dynamics and Coding

Author: Douglas Lind,Brian Marcus

Publisher: Cambridge University Press

ISBN: 9780521551243

Category: Mathematics

Page: 516

View: 9692

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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An Introduction To Chaotic Dynamical Systems

Author: Robert Devaney

Publisher: CRC Press

ISBN: 0429981937

Category: Science

Page: 360

View: 8395

The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
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Symbolic Dynamics

One-sided, Two-sided and Countable State Markov Shifts

Author: Bruce P. Kitchens

Publisher: Springer Science & Business Media

ISBN: 3642588220

Category: Mathematics

Page: 254

View: 5421

Nearly one hundred years ago Jacques Hadamard used infinite sequences of symbols to analyze the distribution of geodesics on certain surfaces. That was the beginning of symbolic dynamics. In the 1930's and 40's Arnold Hedlund and Marston Morse again used infinite sequences to investigate geodesics on surfaces of negative curvature. They coined the term symbolic dynamics and began to study sequence spaces with the shift transformation as dynamical systems. In the 1940's Claude Shannon used sequence spaces to describe infor mation channels. Since that time symbolic dynamics has been used in ergodic theory, topological dynamics, hyperbolic dynamics, information theory and complex dynamics. Symbolic dynamical systems with a finite memory are stud ied in this book. They are the topological Markov shifts. Each can be defined by transition rules and the rules can be summarized by a transition matrix. The study naturally divides into two parts. The first part is about topological Markov shifts where the alphabet is finite. The second part is concerned with topological Markov shifts whose alphabet is count ably infinite. The techniques used in the two cases are quite different. When the alphabet is finite most of the methods are combinatorial or algebraic. When the alphabet is infinite the methods are much more analytic. This book grew from notes for a graduate course taught at Wesleyan Uni versity in the fall of 1994 and is intended as a graduate text and as a reference book for mathematicians working in related fields.
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A First Course in Dynamics

with a Panorama of Recent Developments

Author: Boris Hasselblatt,Anatole Katok

Publisher: Cambridge University Press

ISBN: 1316582655

Category: Mathematics

Page: N.A

View: 3242

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.
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Symbolic Dynamics and Its Applications

American Mathematical Society, Short Course, January 4-5, 2002, San Diego, California

Author: Susan G. Williams

Publisher: American Mathematical Soc.

ISBN: 0821831577

Category: Mathematics

Page: 156

View: 8082

Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in their own right. Today, symbolic dynamics has expanded to encompass multi-dimensional arrays of symbols and has found diverse applications both within and beyond mathematics. This volume is based on the AMS Short Course on Symbolic Dynamics and its Applications. It contains introductory articles on the fundamental ideas of the field and on some of its applications. Topics include the use of symbolic dynamics techniques in coding theory and in complex dynamics, the relation between the theory of multi-dimensional systems and the dynamics of tilings, and strong shift equivalence theory. Contributors to the volume are experts in the field and are clear expositors. The book is suitable for graduate students and research mathematicians interested in symbolic dynamics and its applications.
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Introduction to Dynamical Systems

Author: Michael Brin,Garrett Stuck

Publisher: Cambridge University Press

ISBN: 9781139433976

Category: Mathematics

Page: N.A

View: 8531

This book provides a broad introduction to the subject of dynamical systems, suitable for a one- or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to such areas as number theory, data storage, and Internet search engines. This book grew out of lecture notes from the graduate dynamical systems course at the University of Maryland, College Park, and reflects not only the tastes of the authors, but also to some extent the collective opinion of the Dynamics Group at the University of Maryland, which includes experts in virtually every major area of dynamical systems.
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Introduction to Experimental Mathematics

Author: Søren Eilers,Rune Johansen

Publisher: Cambridge University Press

ISBN: 1107156130

Category: Computers

Page: 320

View: 1462

Mathematics is not, and never will be, an empirical science, but mathematicians are finding that the use of computers and specialized software allows the generation of mathematical insight in the form of conjectures and examples, which pave the way for theorems and their proofs. In this way, the experimental approach to pure mathematics is revolutionizing the way research mathematicians work. As the first of its kind, this book provides material for a one-semester course in experimental mathematics that will give students the tools and training needed to systematically investigate and develop mathematical theory using computer programs written in Maple. Accessible to readers without prior programming experience, and using examples of concrete mathematical problems to illustrate a wide range of techniques, the book gives a thorough introduction to the field of experimental mathematics, which will prepare students for the challenge posed by open mathematical problems.
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Dynamic Web Programming and HTML5

Author: Paul S. Wang

Publisher: CRC Press

ISBN: 1439871825

Category: Computers

Page: 664

View: 2964

With organizations and individuals increasingly dependent on the Web, the need for competent, well-trained Web developers and maintainers is growing. Helping readers master Web development, Dynamic Web Programming and HTML5 covers specific Web programming languages, APIs, and coding techniques and provides an in-depth understanding of the underlying concepts, theory, and principles. The author leads readers through page structuring, page layout/styling, user input processing, dynamic user interfaces, database-driven websites, and mobile website development. After an overview of the Web and Internet, the book focuses on the new HTML5 and its associated open Web platform standards. It covers the HTML5 markup language and DOM, new elements for structuring Web documents and forms, CSS3, and important JavaScript APIs associated with HTML5. Moving on to dynamic page generation and server-side programming with PHP, the text discusses page templates, form processing, session control, user login, database access, and server-side HTTP requests. It also explores more advanced topics such as XML and PHP/MySQL. Suitable for a one- or two-semester course at the advanced undergraduate or beginning graduate level, this comprehensive and up-to-date guide helps readers learn modern Web technologies and their practical applications. Numerous examples illustrate how the programming techniques and other elements work together to achieve practical goals. Online Resource Encouraging hands-on practice, the book’s companion website at http://dwp.sofpower.com helps readers gain experience with the technologies and techniques involved in building good sites. Maintained by the author, the site offers: Live examples organized by chapter and cross-referenced in the text Programs from the text bundled in a downloadable code package Searchable index and appendices Ample resource listings and information updates
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Statistical Techniques in Business and Economics

Author: Douglas Lind

Publisher: McGraw-Hill Higher Education

ISBN: 0077639723

Category: Business & Economics

Page: 864

View: 5615

Lind/Marchal/Wathen is a perennial market best seller due to its comprehensive coverage of statistical concepts and methods delivered in a student friendly, step-by-step format. The text presents concepts clearly and succinctly with a conversational writing style and illustrates concepts through the liberal use of business-focused examples that are relevant to the current world of a college student. Known as a “student's text,” Lind's supporting pedagogy includes self-reviews, cumulative exercises, and coverage of software applications including Excel, Minitab, and MegaStat for Excel. And now, McGraw-Hill’s adaptive learning component, LearnSmart, provides assignable modules that help students master chapter core concepts and come to class more prepared. In addition, resources within Connect Plus help students solve problems and apply what they’ve learned. Lind’s real-world examples, comprehensive coverage, and superior pedagogy combine with a complete digital solution to help students achieve higher outcomes in the course.
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Symbolic Dynamics and Its Applications

Author: Roy L. Adler,Peter Walters

Publisher: American Mathematical Soc.

ISBN: 0821851462

Category: Mathematics

Page: 451

View: 2202

This volume contains the proceedings of the conference, Symbolic Dynamics and its Applications, held at Yale University in the summer of 1991 in honor of Roy L. Adler on his sixtieth birthday. The conference focused on symbolic dynamics and its applications to other fields, including ergodic theory, smooth dynamical systems, information theory, automata theory, and statistical mechanics. One hundred thirty-nine participants attended from thirteen countries, representing mathematics, applied mathematics, electrical engineering, and physics departments in universities and in industry. Featuring a range of contributions from some of the leaders in the field, this volume presents an excellent overview of the subject.
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Modern Dynamical Systems and Applications

Author: Michael Brin,Boris Hasselblatt,Yakov Pesin

Publisher: Cambridge University Press

ISBN: 9780521840736

Category: Mathematics

Page: 458

View: 6870

This volume presents a wide cross-section of current research in the theory of dynamical systems and contains articles by leading researchers, including several Fields medalists, in a variety of specialties. These are surveys, usually with new results included, as well as research papers that are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, applications. The target audience includes dynamicists, who will find new results in their own specialty as well as surveys in others, and mathematicians from other disciplines wholook for a sample of current developments in ergodic theory and dynamical systems.
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One-Dimensional Dynamics

Author: Welington de Melo,Sebastian van Strien

Publisher: Springer Science & Business Media

ISBN: 3642780431

Category: Mathematics

Page: 606

View: 5939

One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).
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Sets for Mathematics

Author: F. William Lawvere,Robert Rosebrugh

Publisher: Cambridge University Press

ISBN: 9780521010603

Category: Mathematics

Page: 261

View: 4863

In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
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Dynamical Systems and Ergodic Theory

Author: Mark Pollicott,Michiko Yuri

Publisher: Cambridge University Press

ISBN: 9780521575997

Category: Mathematics

Page: 179

View: 8280

This book is essentially a self-contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a master's level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der Waerden's theorem and Szemerdi's theorem).
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Algebraic Combinatorics on Words

Author: M. Lothaire

Publisher: Cambridge University Press

ISBN: 9780521812207

Category: Mathematics

Page: 504

View: 1625

Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.
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Modeling and Analysis of Dynamic Systems, Third Edition

Author: Ramin S. Esfandiari,Bei Lu

Publisher: CRC Press

ISBN: 1351751646

Category: Technology & Engineering

Page: 595

View: 2635

Modeling and Analysis of Dynamic Systems, Third Edition introduces MATLAB®, Simulink®, and SimscapeTM and then utilizes them to perform symbolic, graphical, numerical, and simulation tasks. Written for senior level courses/modules, the textbook meticulously covers techniques for modeling a variety of engineering systems, methods of response analysis, and introductions to mechanical vibration, and to basic control systems. These features combine to provide students with a thorough knowledge of the mathematical modeling and analysis of dynamic systems. The Third Edition now includes Case Studies, expanded coverage of system identification, and updates to the computational tools included.
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Developments in Language Theory

19th International Conference, DLT 2015, Liverpool, UK, July 27-30, 2015, Proceedings.

Author: Igor Potapov

Publisher: Springer

ISBN: 3319215000

Category: Computers

Page: 440

View: 796

This book constitutes the proceedings of the 19th International Conference on Developments in Language Theory, DLT 2015, held in Liverpool, UK. The 31 papers presented together with 5 invited talks were carefully reviewed and selected from 54 submissions. Its scope is very general and includes, among others, the following topics and areas: combinatorial and algebraic properties of words and languages, grammars, acceptors and transducers for strings, trees, graphs, arrays, algebraic theories for automata and languages, codes, efficient text algorithms, symbolic dynamics, decision problems, relationships to complexity theory and logic, picture description and analysis, polyominoes and bidimensional patterns, cryptography, concurrency, cellular automata, bio-inspired computing, and quantum computing.
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Cellular Automata and Groups

Author: Tullio Ceccherini-Silberstein,Michel Coornaert

Publisher: Springer Science & Business Media

ISBN: 9783642140341

Category: Computers

Page: 440

View: 1791

Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.
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