Overview
- Provides an entry for graduate students into an active field of research
- Each chapter includes exercises, examples, and figures
- Will become a standard reference for researchers in the field
- Contains a description of many known results and conjectures, together with an extensive bibliography
- Includes supplementary material: sn.pub/extras
Part of the book series: Graduate Texts in Mathematics (GTM, volume 241)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Reviews
From the reviews:
"The connections between dynamical systems and number theory arise in many different ways. … This remarkable book unifies and clarifies one of these connections, in the setting of what might be called ‘Arithmetic Dynamical Systems’. … suitable for many graduate students. … This book should be of great interest to anyone interested in dynamics or number theory, and will attract them into this fascinating field. Not for the first time, the mathematical community owes the author thanks for a wonderful book … ." (Thomas Ward, Mathematical Reviews, Issue 2008 c)
"The Arithmetic of Dynamical Systems is intended for an audience of researchers and graduate students in number theory. … The book could easily be used for a special-topics graduate course. … will serve not only as an excellent introduction to the Diophantine aspects of dynamics for the uninitiated, but also as a valuable reference for experts in the field. It is certain to be an essential resource for anyone interested in this active and growing area of research." (Rob Benedetto, MathDL, January, 2008)
"The Arithmetic of Dynamical Systems arrives with auspicious timing. ...[T]he field is young enough that there are few, if any, other such comprehensive introductions to the subject. With a growing number of graduate students and established researchers trying to learn the subject, such a clear exposition comes none too soon.
The book is well organized and well written.... Ideas and intuitions are conveyed clearly, but at the same time, the presntation is completely rigorous. ... Number theorists interested in studying dynamics will find this book to be both an excellent introduction and a valuable reference for the subject." (Rob Bendetto, Bulletins of the American Mathematical Society, December 2008)
“This textbook introduces the reader to the dynamics of a rational function acting on the projective line over a number field. … Thebook is aimed mostly at number theorists. … This volume will provide a generation of number theorists with a comprehensive introduction to an intriguing field, whose results might make possible advances in other parts of number theory.” (C. Baxa, Monatshefte für Mathematik, Vol. 158 (3), November, 2009)
Authors and Affiliations
Bibliographic Information
Book Title: The Arithmetic of Dynamical Systems
Authors: Joseph H. Silverman
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-0-387-69904-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2007
Hardcover ISBN: 978-0-387-69903-5Published: 06 June 2007
Softcover ISBN: 978-1-4419-2417-9Published: 19 November 2010
eBook ISBN: 978-0-387-69904-2Published: 05 May 2010
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XVI, 511
Number of Illustrations: 11 b/w illustrations
Topics: Dynamical Systems and Ergodic Theory, Data Structures