The Arithmetic of Dynamical Systems
Silverman J. H.
Sold by Majestic Books, Hounslow, United Kingdom
AbeBooks Seller since 19 January 2007
New - Soft cover
Condition: New
Ships from United Kingdom to U.S.A.
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Add to basketSold by Majestic Books, Hounslow, United Kingdom
AbeBooks Seller since 19 January 2007
Condition: New
Quantity: 4 available
Add to basketPrint on Demand pp. 528 11 Illus.
Seller Inventory # 5803120
This book investigates the relatively new subject of Arithmetic Dynamics, which is the study of the number theoretic properties of algebraic numbers or points under repeated application of a polynomial or rational map. Classical discrete dynamics is the study of iteration of functions mapping the complex plane (or real line) to itself. Arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. The viewpoint of this book is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs. As is typical in any subject combining Diophantine problems and geometry, an overarching theme is that at least qualitatively, the geometry determines the arithmetic.
This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function.
A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs. As is typical in any subject combining Diophantine problems and geometry, a fundamental goal is to describe arithmetic properties, at least qualitatively, in terms of underlying geometric structures.
Key features:
- Provides an entry for graduate students into an active field of research
- Provides a standard reference source for researchers
- Includes numerous exercises and examples
- Contains a description of many known results and conjectures, as well as an extensive glossary, bibliography, and index
This graduate-level text assumes familiarity with basic algebraic number theory. Other topics, such as basic algebraic geometry, elliptic curves, nonarchimedean analysis, and the theory of Diophantine approximation, are introduced and referenced as needed. Mathematicians and graduate students will find this text to be an excellent reference.
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