The Arithmetic Of Dynamical Systems

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Advanced Topics in the Arithmetic of Elliptic Curves

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
ISBN 13 : 1461208513
Total Pages : 482 pages
Book Rating : 4.4/5 (612 download)

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

Download or read book Advanced Topics in the Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : J.H. Silverman
Publisher : Springer Science & Business Media
ISBN 13 : 038769904X
Total Pages : 518 pages
Book Rating : 4.3/5 (876 download)

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

Download or read book The Arithmetic of Dynamical Systems written by J.H. Silverman and published by Springer Science & Business Media. This book was released on 2010-05-05 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461418054
Total Pages : 1885 pages
Book Rating : 4.4/5 (614 download)

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

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Invitation to Dynamical Systems

Author : Edward R. Scheinerman
Publisher : Courier Corporation
ISBN 13 : 0486275329
Total Pages : 408 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Invitation to Dynamical Systems by : Edward R. Scheinerman

Download or read book Invitation to Dynamical Systems written by Edward R. Scheinerman and published by Courier Corporation. This book was released on 2013-05-13 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.

Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

Author : Sébastien Ferenczi
Publisher : Springer
ISBN 13 : 3319749080
Total Pages : 434 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by : Sébastien Ferenczi

Download or read book Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics written by Sébastien Ferenczi and published by Springer. This book was released on 2018-06-15 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

Moduli Spaces and Arithmetic Dynamics

Author : Joseph H. Silverman
Publisher : American Mathematical Soc.
ISBN 13 : 0821885030
Total Pages : 151 pages
Book Rating : 4.8/5 (218 download)

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

Download or read book Moduli Spaces and Arithmetic Dynamics written by Joseph H. Silverman and published by American Mathematical Soc.. This book was released on with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamical Systems and Ergodic Theory

Author : Mark Pollicott
Publisher :
ISBN 13 : 9781299733909
Total Pages : pages
Book Rating : 4.7/5 (339 download)

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Book Synopsis Dynamical Systems and Ergodic Theory by : Mark Pollicott

Download or read book Dynamical Systems and Ergodic Theory written by Mark Pollicott and published by . This book was released on 2013-07-13 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.

Applied Algebraic Dynamics

Author : Vladimir Anashin
Publisher : Walter de Gruyter
ISBN 13 : 3110203014
Total Pages : 558 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Applied Algebraic Dynamics by : Vladimir Anashin

Download or read book Applied Algebraic Dynamics written by Vladimir Anashin and published by Walter de Gruyter. This book was released on 2009-06-02 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Heights of Polynomials and Entropy in Algebraic Dynamics

Author : Graham Everest
Publisher : Springer Science & Business Media
ISBN 13 : 1447138988
Total Pages : 217 pages
Book Rating : 4.4/5 (471 download)

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

Download or read book Heights of Polynomials and Entropy in Algebraic Dynamics written by Graham Everest and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Chaos and Dynamical Systems

Author : David P. Feldman
Publisher : Princeton University Press
ISBN 13 : 0691161526
Total Pages : 262 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Chaos and Dynamical Systems by : David P. Feldman

Download or read book Chaos and Dynamical Systems written by David P. Feldman and published by Princeton University Press. This book was released on 2019-08-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.

Number Theory and Dynamical Systems

Author : M. M. Dodson
Publisher : Cambridge University Press
ISBN 13 : 0521369193
Total Pages : 185 pages
Book Rating : 4.5/5 (213 download)

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

Download or read book Number Theory and Dynamical Systems written by M. M. Dodson and published by Cambridge University Press. This book was released on 1989-11-09 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics

Author : David Carfi
Publisher : American Mathematical Soc.
ISBN 13 : 0821891472
Total Pages : 410 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics by : David Carfi

Download or read book Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics written by David Carfi and published by American Mathematical Soc.. This book was released on 2013-10-22 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.

The Arithmetic of Elliptic Curves

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
ISBN 13 : 1475719205
Total Pages : 414 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Arithmetic of Elliptic Curves by : Joseph H. Silverman

Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Topics in Dynamics and Ergodic Theory

Author : Sergey Bezuglyi
Publisher : Cambridge University Press
ISBN 13 : 9780521533652
Total Pages : 276 pages
Book Rating : 4.5/5 (336 download)

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Book Synopsis Topics in Dynamics and Ergodic Theory by : Sergey Bezuglyi

Download or read book Topics in Dynamics and Ergodic Theory written by Sergey Bezuglyi and published by Cambridge University Press. This book was released on 2003-12-08 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.

Moduli Spaces and Arithmetic Dynamics

Author : Joseph H. Silverman
Publisher : Amer Mathematical Society
ISBN 13 : 9780821875827
Total Pages : 140 pages
Book Rating : 4.8/5 (758 download)

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

Download or read book Moduli Spaces and Arithmetic Dynamics written by Joseph H. Silverman and published by Amer Mathematical Society. This book was released on 2012 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies moduli problems associated to algebraic dynamical systems. It is an expanded version of the notes for a series of lectures delivered at a workshop on Moduli Spaces and the Arithmetic of Dynamical Systems at the Bellairs Research Institute, Barbados, in 2010. The author's goal is to provide an overview, with enough details and pointers to the existing literature, to give the reader an entry into this exciting area of current research. Topics covered include: (1) Construction and properties of dynamical moduli spaces for self-maps of projective space. (2) Dynatomic modular curves for the space of quadratic polynomials. (3) The theory of canonical heights associated to dynamical systems. (4) Special loci in dynamical moduli spaces, in particular the locus of post-critically finite maps. (5) Field of moduli and fields of definition for dynamical systems.

Dynamical Aspects of Teichmüller Theory

Author : Carlos Matheus Silva Santos
Publisher : Springer
ISBN 13 : 3319921592
Total Pages : 122 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Dynamical Aspects of Teichmüller Theory by : Carlos Matheus Silva Santos

Download or read book Dynamical Aspects of Teichmüller Theory written by Carlos Matheus Silva Santos and published by Springer. This book was released on 2018-07-09 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a remarkable contribution to the literature on dynamical systems and geometry. It consists of a selection of work in current research on Teichmüller dynamics, a field that has continued to develop rapidly in the past decades. After a comprehensive introduction, the author investigates the dynamics of the Teichmüller flow, presenting several self-contained chapters, each addressing a different aspect on the subject. The author includes innovative expositions, all the while solving open problems, constructing examples, and supplementing with illustrations. This book is a rare find in the field with its guidance and support for readers through the complex content of moduli spaces and Teichmüller Theory. The author is an internationally recognized expert in dynamical systems with a talent to explain topics that is rarely found in the field. He has created a text that would benefit specialists in, not only dynamical systems and geometry, but also Lie theory and number theory.

Noncommutative Geometry and Number Theory

Author : Caterina Consani
Publisher : Springer Science & Business Media
ISBN 13 : 3834803529
Total Pages : 374 pages
Book Rating : 4.8/5 (348 download)

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Book Synopsis Noncommutative Geometry and Number Theory by : Caterina Consani

Download or read book Noncommutative Geometry and Number Theory written by Caterina Consani and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.