The Arithmetic of Dynamical Systems

J. H. Silverman

ISBN 10: 0387699031 / ISBN 13: 9780387699035

Editore: Springer New York, Springer New York Jun 2007, 2007

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Neuware -This book is designed to provide a path for the reader into an amalgamation oftwo venerable areas ofmathematics, Dynamical Systems and Number Theory. Many of the motivating theorems and conjectures in the new subject of Arithmetic Dynamics may be viewed as the transposition ofclassical results in the theory ofDiophantine equations to the setting of discrete dynamical systems, especially to the iteration theory ofmaps on the projective line and other algebraic varieties. Although there is no precise dictionary connecting the two areas, the reader will gain a flavor of the correspondence from the following associations: Diophantine Equations Dynamical Systems rational and integral rational and integral points on varieties points in orbits torsion points on periodic and preperiodic abelian varieties points ofrational maps There are a variety of topics covered in this volume, but inevitably the choice reflects the author's tastes and interests. Many related areas that also fall under the heading ofarithmetic or algebraic dynamics have been omitted in order to keep the book to a manageable length. A brief list of some of these omitted topics may be found in the introduction. Online Resources The reader will find additonal material, references and errata at math. brown. ectu/-jhs/ADSHome. html Acknowledgments The author has consulted a great many sources in writing this book. Every attempt has been made to give proper attribution for all but the most standard results.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 528 pp. Englisch.

Codice articolo 9780387699035

Dati bibliografici

• Titolo: The Arithmetic of Dynamical Systems
• Editore: Springer New York, Springer New York Jun 2007
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 0387699031
• ISBN 13: 9780387699035
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 34 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 34 millimetri di profondità
• Peso: 951 grammi

Descrizione articolo

Riassunto

Arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. This book presents an introduction to the discipline of arithmetic dynamics.

Dalla quarta di copertina

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.