The Arithmetic of Dynamical Systems
By: Silverman, Joseph H [author.].
Contributor(s): SpringerLink (Online service).
Material type:
BookSeries: Graduate Texts in Mathematics: 241Publisher: New York, NY : Springer New York, 2007.Description: XVI, 511 p. 11 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387699042.Subject(s): Mathematics | Data structures (Computer science) | Dynamics | Ergodic theory | Mathematics | Dynamical Systems and Ergodic Theory | Data StructuresDDC classification: 515.39 | 515.48 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
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E books
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PK Kelkar Library, IIT Kanpur | Available | EBK9203 |
An Introduction to Classical Dynamics -- Dynamics over Local Fields: Good Reduction -- Dynamics over Global Fields -- Families of Dynamical Systems -- Dynamics over Local Fields: Bad Reduction -- Dynamics Associated to Algebraic Groups -- Dynamics in Dimension Greater Than One.
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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