Number Theory And Dynamical Systems

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Number Theory and Dynamical Systems

M. M. Dodson
Number Theory and Dynamical Systems Book PDF

Author : M. M. Dodson
Publisher : Cambridge University Press
Page : 185 pages
File Size : 40,5 Mb
Release : 1989-11-09
Category : Mathematics
ISBN : 9780521369190

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Number Theory and Dynamical Systems by M. M. Dodson Pdf

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.

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

Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics Book PDF

Author : Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Publisher : Springer
Page : 434 pages
File Size : 40,9 Mb
Release : 2018-06-15
Category : Mathematics
ISBN : 9783319749082

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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk Pdf

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.

Advanced Topics in the Arithmetic of Elliptic Curves

Joseph H. Silverman
Advanced Topics in the Arithmetic of Elliptic Curves Book PDF

Author : Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 42,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461208518

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

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.

Number Theory and Dynamical Systems

M. M. Dodson,J. A. G. Vickers,Savilian Professor of Geometry N J Hitchin
Number Theory and Dynamical Systems Book PDF

Author : M. M. Dodson,J. A. G. Vickers,Savilian Professor of Geometry N J Hitchin
Publisher : Unknown
Page : 181 pages
File Size : 53,8 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107361559

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Number Theory and Dynamical Systems by M. M. Dodson,J. A. G. Vickers,Savilian Professor of Geometry N J Hitchin Pdf

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.

The Unreasonable Effectiveness of Number Theory

Stefan Andrus Burr,George E. Andrews
The Unreasonable Effectiveness of Number Theory Book PDF

Author : Stefan Andrus Burr,George E. Andrews
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 45,9 Mb
Release : 1992
Category : Mathematics
ISBN : 0821855018

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The Unreasonable Effectiveness of Number Theory by Stefan Andrus Burr,George E. Andrews Pdf

"Number theory is one of the oldest and noblest branches of mathematics; indeed, it was already ancient in the time of Euclid...for almost all of its history it has seemed to be among the purest branches of mathematics. It is only within the last few decades that a large number of applications have been encountered, at least by the mathematical community. The applications to cryptology are now famous; but it is not as well known that number theory has found an enormous number and variety of real-world applications in many different fields." - From the Preface This book is based on the AMS Short Course, The Unreasonable Effectiveness of Number Theory, held in Orono, Maine, in August 1991. This Short Course provided some views into the great breadth of application of number theory outside cryptology and highlighted the power and applicability of number-theoretic ideas. Because number theory is one of the most accessible areas of mathematics, this book will appeal to a general mathematical audience as well as to researchers in other areas of science and engineering who wish to learn how number theory is being applied outside of mathematics. All of the chapters are written by leading specialists in number theory and provides excellent introduction to various applications.

Ergodic Theory

Manfred Einsiedler,Thomas Ward
Ergodic Theory Book PDF

Author : Manfred Einsiedler,Thomas Ward
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 45,9 Mb
Release : 2010-09-11
Category : Mathematics
ISBN : 9780857290212

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Ergodic Theory by Manfred Einsiedler,Thomas Ward Pdf

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

Sequences, Groups, and Number Theory

Valérie Berthé,Michel Rigo
Sequences Groups and Number Theory Book PDF

Author : Valérie Berthé,Michel Rigo
Publisher : Birkhäuser
Page : 578 pages
File Size : 48,7 Mb
Release : 2018-04-09
Category : Mathematics
ISBN : 9783319691527

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Sequences, Groups, and Number Theory by Valérie Berthé,Michel Rigo Pdf

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Dynamics and Analytic Number Theory

Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff
Dynamics and Analytic Number Theory Book PDF

Author : Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff
Publisher : Cambridge University Press
Page : 341 pages
File Size : 42,6 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781107552371

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Dynamics and Analytic Number Theory by Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff Pdf

Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.

Mathematics of Complexity and Dynamical Systems

Robert A. Meyers
Mathematics of Complexity and Dynamical Systems Book PDF

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 52,9 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054

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Mathematics of Complexity and Dynamical Systems by Robert A. Meyers Pdf

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.

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

Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics Book PDF

Author : Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Publisher : Springer
Page : 434 pages
File Size : 54,6 Mb
Release : 2018-06-16
Category : Mathematics
ISBN : 3319749072

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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk Pdf

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.

Geometric Theory of Dynamical Systems

J. Jr. Palis,W. de Melo
Geometric Theory of Dynamical Systems Book PDF

Author : J. Jr. Palis,W. de Melo
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461257035

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Geometric Theory of Dynamical Systems by J. Jr. Palis,W. de Melo Pdf

... cette etude qualitative (des equations difj'erentielles) aura par elle-m me un inter t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations.

The Arithmetic of Dynamical Systems

J.H. Silverman
The Arithmetic of Dynamical Systems Book PDF

Author : J.H. Silverman
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 41,5 Mb
Release : 2010-05-05
Category : Mathematics
ISBN : 9780387699042

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The Arithmetic of Dynamical Systems by J.H. Silverman Pdf

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.

Recurrence in Ergodic Theory and Combinatorial Number Theory

Harry Furstenberg
Recurrence in Ergodic Theory and Combinatorial Number Theory Book PDF

Author : Harry Furstenberg
Publisher : Princeton University Press
Page : 216 pages
File Size : 47,5 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400855162

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Recurrence in Ergodic Theory and Combinatorial Number Theory by Harry Furstenberg Pdf

Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Dynamical Numbers: Interplay between Dynamical Systems and Number Theory

S. F. Koli︠a︡da
Dynamical Numbers Interplay between Dynamical Systems and Number Theory Book PDF

Author : S. F. Koli︠a︡da
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 54,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849583

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Dynamical Numbers: Interplay between Dynamical Systems and Number Theory by S. F. Koli︠a︡da Pdf

This volume contains papers from the special program and international conference on Dynamical Numbers which were held at the Max-Planck Institute in Bonn, Germany in 2009. These papers reflect the extraordinary range and depth of the interactions between ergodic theory and dynamical systems and number theory. Topics covered in the book include stationary measures, systems of enumeration, geometrical methods, spectral methods, and algebraic dynamical systems.

Dynamical Systems, Number Theory and Applications

Thomas Hagen,Florian Rupp,Jrgen Scheurle
Dynamical Systems Number Theory and Applications Book PDF

Author : Thomas Hagen,Florian Rupp,Jrgen Scheurle
Publisher : World Scientific
Page : 279 pages
File Size : 43,5 Mb
Release : 2016
Category : Mathematics
ISBN : 9789814699877

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Dynamical Systems, Number Theory and Applications by Thomas Hagen,Florian Rupp,Jrgen Scheurle Pdf

"This volume consists of a selection of research-type articles on dynamical systems, evolution equations, analytic number theory and closely related topics. A strong emphasis is on a fair balance between theoretical and more applied work, thus spanning the chasm between abstract insight and actual application. Several of the articles are expected to be in the intersection of dynamical systems theory and number theory. One article will likely relate the topics presented to the academic achievements and interests of Prof. Leutbecher and shed light on common threads among all the contributions."--