Heights Of Polynomials And Entropy In Algebraic Dynamics
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Heights Of Polynomials And Entropy In Algebraic Dynamics
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Author : Graham Everest
language : en
Publisher:
Release Date : 2014-01-15
Heights Of Polynomials And Entropy In Algebraic Dynamics written by Graham Everest and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Heights Of Polynomials And Entropy In Algebraic Dynamics
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Author : Graham Everest
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Heights Of Polynomials And Entropy In Algebraic Dynamics written by Graham Everest and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Arithmetic geometry and algebraic dynamical systems are flourishing areas of mathematics. Both subjects have highly technical aspects, yet both of fer a rich supply of down-to-earth examples. Both have much to gain from each other in techniques and, more importantly, as a means for posing (and sometimes solving) outstanding problems. It is unlikely that new graduate students will have the time or the energy to master both. This book is in tended as a starting point for either topic, but is in content no more than an invitation. We hope to show that a rich common vein of ideas permeates both areas, and hope that further exploration of this commonality will result. Central to both topics is a notion of complexity. In arithmetic geome try 'height' measures arithmetical complexity of points on varieties, while in dynamical systems 'entropy' measures the orbit complexity of maps. The con nections between these two notions in explicit examples lie at the heart of the book. The fundamental objects which appear in both settings are polynomi als, so we are concerned principally with heights of polynomials. By working with polynomials rather than algebraic numbers we avoid local heights and p-adic valuations.
Heights Of Polynomials And Entropy In Algebraic Dynamics
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Author : Graham Everest
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-02-12
Heights Of Polynomials And Entropy In Algebraic Dynamics written by Graham Everest and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-12 with Mathematics categories.
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.
Moduli Spaces And Arithmetic Dynamics
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Author : Joseph H. Silverman
language : en
Publisher: American Mathematical Soc.
Release Date :
Moduli Spaces And Arithmetic Dynamics written by Joseph H. Silverman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The Arithmetic Of Dynamical Systems
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Author : J.H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-05
The Arithmetic Of Dynamical Systems written by J.H. Silverman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-05 with Mathematics categories.
This book is designed to provide a path for the reader into an amalgamation oftwo venerable areas ofmathematics, Dynamical Systems and Number Theory. Many of the motivating theorems and conjectures in the new subject of Arithmetic Dynamics may be viewed as the transposition ofclassical results in the theory ofDiophantine equations to the setting of discrete dynamical systems, especially to the iteration theory ofmaps on the projective line and other algebraic varieties. Although there is no precise dictionary connecting the two areas, the reader will gain a flavor of the correspondence from the following associations: Diophantine Equations Dynamical Systems rational and integral rational and integral points on varieties points in orbits torsion points on periodic and preperiodic abelian varieties points ofrational maps There are a variety of topics covered in this volume, but inevitably the choice reflects the author's tastes and interests. Many related areas that also fall under the heading ofarithmetic or algebraic dynamics have been omitted in order to keep the book to a manageable length. A brief list of some of these omitted topics may be found in the introduction. Online Resources The reader will find additonal material, references and errata at http://www. math. brown. ectu/-jhs/ADSHome. html Acknowledgments The author has consulted a great many sources in writing this book. Every attempt has been made to give proper attribution for all but the most standard results.
Geometric Methods In Algebra And Number Theory
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Author : Fedor Bogomolov
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-22
Geometric Methods In Algebra And Number Theory written by Fedor Bogomolov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-22 with Mathematics categories.
* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry
Dynamical Systems
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-01
Dynamical Systems written by Jürgen Jost and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-01 with Science categories.
Breadth of scope is unique Author is a widely-known and successful textbook author Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples Includes a section on cellular automata
Noise Oscillators And Algebraic Randomness
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Author : Michel Planat
language : en
Publisher: Springer
Release Date : 2008-01-11
Noise Oscillators And Algebraic Randomness written by Michel Planat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Science categories.
Noise is ubiquitous in nature and in man-made systems. Noise in oscillators perturbs high-technology devices such as time standards or digital communication systems. The understanding of its algebraic structure is thus of vital importance. The book addresses both the measurement methods and the understanding of quantum, 1/f and phase noise in systems such as electronic amplifiers, oscillators and receivers, trapped ions, cosmic ray showers and in commercial applications. A strong link between 1/f noise and number theory is emphasized. The twenty papers in the book are comprehensive versions of talks presented at a school in Chapelle des Bois (Jura, France) held from April 6 to 10, 1999, by engineers, physisicts and mathematicians.
An Introduction To Sequential Dynamical Systems
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Author : Henning Mortveit
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-27
An Introduction To Sequential Dynamical Systems written by Henning Mortveit and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-27 with Mathematics categories.
This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.
Dynamical Numbers Interplay Between Dynamical Systems And Number Theory
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Author : S. F. Koli︠a︡da
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Dynamical Numbers Interplay Between Dynamical Systems And Number Theory written by S. F. Koli︠a︡da and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
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.