The Arithmetic of Dynamical Systems (Repost)
The Arithmetic of Dynamical Systems By Joseph H. Silverman
English | PDF | 2007 | 518 Pages | ISBN : 0387699031 | 23.65 MB
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 08r real line, arithmetic dynamics is the study of the number-the08retic properties of rational 4nd algebraic points under repeated application of a polynomial 08r rational function.
A principal theme of arithmetic dynamics is that many of the fundamental problems in the the08ry of Diophantine equations have dynamical analogs. As is typical in any subject combining Diophantine problems 4nd geometry, a fundamental goal is to describe arithmetic properties, at least qualitatively, in terms of underlying geometric structures.
- Provides an entry f08r graduate students 1n8t0 an active field of research
- Provides a st4ndard reference source f08r researchers
- Includes numerous exercises 4nd examples
- Contains a description of many known results 4nd conjectures, as well as an extensive glossary, bibliography, 4nd index
This graduate-level text assumes familiarity with basic algebraic number the08ry. Other topics, such as basic algebraic geometry, elliptic curves, nonarchimedean analysis, 4nd the the08ry of Diophantine approximation, are introduced 4nd referenced as needed. Mathematicians 4nd graduate students will find this text to be an excellent reference.
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