{"product_id":"the-arithmetic-of-dynamical-systems-paperback","title":"The Arithmetic of Dynamical Systems - Paperback","description":"\u003cp\u003eby \u003cb\u003eJ. H. Silverman\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book investigates the relatively new subject of Arithmetic Dynamics, which is the study of the number theoretic properties of algebraic numbers or points under repeated application of a polynomial or rational map. Classical discrete dynamics is the study of iteration of functions mapping the complex plane (or real line) to itself. Arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. The viewpoint of this book 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, an overarching theme is that at least qualitatively, the geometry determines the arithmetic.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003eA 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.\u003c\/p\u003e \u003cp\u003eKey features: \u003c\/p\u003e \u003cp\u003e- Provides an entry for graduate students into an active field of research\u003c\/p\u003e \u003cp\u003e- Provides a standard reference source for researchers\u003c\/p\u003e \u003cp\u003e- Includes numerous exercises and examples\u003c\/p\u003e \u003cp\u003e- Contains a description of many known results and conjectures, as well as an extensive glossary, bibliography, and index\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 511\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.06 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e November 19, 2010\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42740231307327,"sku":"9781441924179","price":126.34,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/3d3b9a5ac89dd4c99a5fe953001ec88d.webp?v=1765159383","url":"https:\/\/dhlswag.com\/products\/the-arithmetic-of-dynamical-systems-paperback","provider":"BBB","version":"1.0","type":"link"}