000			02454nmm a22002415i 4500
005			20230705150638.0
008			100504s2007 xxu| s |||| 0|eng d
020			_a9780387699042 _9978-0-387-69904-2
082			_a515.39 _223
100			_aSilverman, J.H. _920535
245	1	4	_aThe Arithmetic of Dynamical Systems _h[electronic resource] / _cby J.H. Silverman.
250			_a1st ed. 2007.
260			_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2007.
300			_aXVI, 511 p. 11 illus. _bonline resource.
505			_aAn 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.
520			_aThis 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.
650			_aDynamical systems. _920536
650			_aArtificial intelligence-Data processing. _920537
650			_aDynamical Systems. _920538
650			_aData Science. _920539
856			_uhttps://doi.org/10.1007/978-0-387-69904-2
942			_cEBK
999			_c13652 _d13652