Nantilus
The Arithmetic of Dynamical Systems
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 poin...
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| Auteur principal : | |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | The Arithmetic of Dynamical Systems / by Joseph H. Silverman. |
| Édition : | 1st ed. 2007. |
| Publié : |
New York, NY :
Springer New York
, [20..] Cham : Imprint: Springer Springer Nature |
| Collection : | Graduate texts in mathematics (Internet) ; 241 |
| Titre de l'ensemble : | Graduate Texts in Mathematics vol. 241 |
| Accès en ligne : |
Accès Nantes Université
Accès direct soit depuis les campus via le réseau ou le wifi eduroam soit à distance avec un compte @etu.univ-nantes.fr ou @univ-nantes.fr |
| Note sur l'URL : | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex |
| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | 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 |
| Sujets : | |
| Documents associés : | Autre format:
The arithmetic of dynamical systems |
| Résumé : | 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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| ISBN : | 978-0-387-69904-2 |
| DOI : | 10.1007/978-0-387-69904-2 |