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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. --- Dynamical Systems and Ergodic Theory. --- Differentiable dynamical systems. --- Mathématiques --- Dynamique différentiable --- Dynamics --- Number theory --- Applied Mathematics --- Calculus --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Number study --- Numbers, Theory of --- Dynamical systems --- Kinetics --- Data structures (Computer science). --- Dynamics. --- Ergodic theory. --- Data Structures. --- Algebra --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Data structures (Computer scienc. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Data structures (Computer science) --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems. --- Artificial intelligence --- Dynamical Systems. --- Data Science. --- Data processing.