03116nam a22004335i 4500 978-0-387-69904-2 DE-He213 20260521091933.0 cr nn 008mamaa 100504s2007 xxu| s |||| 0|eng d 9780387699042 99780387699042 10.1007/978-0-387-69904-2 doi CICY 515.39 23 515.48 23 Silverman, Joseph H. author. The Arithmetic of Dynamical Systems [recurso electrónico] / by Joseph H. Silverman. New York, NY : Springer New York, 2007. IX, 511 p. 11 illus. online resource. text txt rdacontent computer c rdamedia recurso en línea cr rdacarrier text file PDF rda Graduate Texts in Mathematics, 0072-5285 ; 241 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. MATHEMATICS. DIFFERENTIABLE DYNAMICAL SYSTEMS. MATHEMATICS. DYNAMICAL SYSTEMS AND ERGODIC THEORY. SpringerLink (Online service) Springer eBooks Printed edition: 9780387699035 Graduate Texts in Mathematics, 0072-5285 ; 241 http://dx.doi.org/10.1007/978-0-387-69904-2 Ver el texto completo en las instalaciones del CICY ddc ER 34077 34077 0 0 ddc 0 0 LE CICY CICY EL 2025-07-10 0 515.39 | 515.48 2025-07-10 08:40:10 2025-07-10 ER