Advanced Topics in the Arithmetic of Elliptic Curves

Advanced Topics in the Arithmetic of Elliptic Curves
Author :
Publisher : Springer Science & Business Media
Total Pages : 482
Release :
ISBN-10 : 9781461208518
ISBN-13 : 1461208513
Rating : 4/5 (18 Downloads)

Synopsis Advanced Topics in the Arithmetic of Elliptic Curves by : Joseph H. Silverman

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.

The Arithmetic of Dynamical Systems

The Arithmetic of Dynamical Systems
Author :
Publisher : Springer Science & Business Media
Total Pages : 518
Release :
ISBN-10 : 9780387699035
ISBN-13 : 0387699031
Rating : 4/5 (35 Downloads)

Synopsis The Arithmetic of Dynamical Systems by : J.H. Silverman

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.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.

Mathematics of Complexity and Dynamical Systems

Mathematics of Complexity and Dynamical Systems
Author :
Publisher : Springer Science & Business Media
Total Pages : 1885
Release :
ISBN-10 : 9781461418054
ISBN-13 : 1461418054
Rating : 4/5 (54 Downloads)

Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Moduli Spaces and Arithmetic Dynamics

Moduli Spaces and Arithmetic Dynamics
Author :
Publisher : American Mathematical Soc.
Total Pages : 151
Release :
ISBN-10 : 9780821885031
ISBN-13 : 0821885030
Rating : 4/5 (31 Downloads)

Synopsis Moduli Spaces and Arithmetic Dynamics by : Joseph H. Silverman

Heights of Polynomials and Entropy in Algebraic Dynamics

Heights of Polynomials and Entropy in Algebraic Dynamics
Author :
Publisher : Springer Science & Business Media
Total Pages : 217
Release :
ISBN-10 : 9781447138983
ISBN-13 : 1447138988
Rating : 4/5 (83 Downloads)

Synopsis Heights of Polynomials and Entropy in Algebraic Dynamics by : Graham Everest

The main theme of this book is the theory of heights as they appear in various guises. This includes a large body of results on Mahlers measure of the height of a polynomial. The authors'approach is very down to earth as they cover the rationals, assuming no prior knowledge of elliptic curves. The chapters include examples and particular computations, with all special calculation included so as to be self-contained. The authors devote space to discussing Mahlers measure and to giving some convincing and original examples to explain this phenomenon. XXXXXXX NEUER TEXT The main theme of this book is the theory of heights as it appears in various guises. To this §End.txt.Int.:, it examines the results of Mahlers measure of the height of a polynomial, which have never before appeared in book form. The authors take a down-to-earth approach that includes convincing and original examples. The book uncovers new and interesting connections between number theory and dynamics and will be interesting to researchers in both number theory and nonlinear dynamics.

The Arithmetic of Dynamical Systems

The Arithmetic of Dynamical Systems
Author :
Publisher : Springer Science & Business Media
Total Pages : 518
Release :
ISBN-10 : 9780387699042
ISBN-13 : 038769904X
Rating : 4/5 (42 Downloads)

Synopsis The Arithmetic of Dynamical Systems by : J.H. Silverman

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.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.

Applied Algebraic Dynamics

Applied Algebraic Dynamics
Author :
Publisher : Walter de Gruyter
Total Pages : 558
Release :
ISBN-10 : 9783110203011
ISBN-13 : 3110203014
Rating : 4/5 (11 Downloads)

Synopsis Applied Algebraic Dynamics by : Vladimir Anashin

This monograph presents recent developments of the theory of algebraic dynamical systems and their applications to computer sciences, cryptography, cognitive sciences, psychology, image analysis, and numerical simulations. The most important mathematical results presented in this book are in the fields of ergodicity, p-adic numbers, and noncommutative groups. For students and researchers working on the theory of dynamical systems, algebra, number theory, measure theory, computer sciences, cryptography, and image analysis.

Dynamical Systems and Ergodic Theory

Dynamical Systems and Ergodic Theory
Author :
Publisher :
Total Pages :
Release :
ISBN-10 : 1299733905
ISBN-13 : 9781299733909
Rating : 4/5 (05 Downloads)

Synopsis Dynamical Systems and Ergodic Theory by : Mark Pollicott

Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.

Number Theory and Dynamical Systems

Number Theory and Dynamical Systems
Author :
Publisher : Cambridge University Press
Total Pages : 185
Release :
ISBN-10 : 9780521369190
ISBN-13 : 0521369193
Rating : 4/5 (90 Downloads)

Synopsis Number Theory and Dynamical Systems by : M. M. Dodson

This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems.

An Introduction To Chaotic Dynamical Systems

An Introduction To Chaotic Dynamical Systems
Author :
Publisher : CRC Press
Total Pages : 280
Release :
ISBN-10 : 9780429981937
ISBN-13 : 0429981937
Rating : 4/5 (37 Downloads)

Synopsis An Introduction To Chaotic Dynamical Systems by : Robert Devaney

The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.