Heights of Polynomials and Entropy in Algebraic Dynamics
Author: Graham Everest
Publisher:
Published: 2014-01-15
Total Pages: 228
ISBN-13: 9781447138990
DOWNLOAD EBOOKPosts
Heights of Polynomials and Entropy in Algebraic Dynamics
Author: Graham Everest
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 217
ISBN-13: 1447138988
DOWNLOAD EBOOKThe 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
Author: Joseph H. Silverman
Publisher: American Mathematical Soc.
Published:
Total Pages: 151
ISBN-13: 0821885030
DOWNLOAD EBOOKThe Arithmetic of Dynamical Systems
Author: J.H. Silverman
Publisher: Springer Science & Business Media
Published: 2010-05-05
Total Pages: 518
ISBN-13: 038769904X
DOWNLOAD EBOOKThis 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.
Geometric Methods in Algebra and Number Theory
Author: Fedor Bogomolov
Publisher: Springer Science & Business Media
Published: 2006-06-22
Total Pages: 365
ISBN-13: 0817644172
DOWNLOAD EBOOK* 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 Numbers: Interplay between Dynamical Systems and Number Theory
Author: S. F. Koli︠a︡da
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 258
ISBN-13: 0821849581
DOWNLOAD EBOOKThis 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
Author: Jürgen Jost
Publisher: Springer Science & Business Media
Published: 2005-08-01
Total Pages: 218
ISBN-13: 9783540229087
DOWNLOAD EBOOKBreadth 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
Research Directions in Number Theory
Author: Alina Bucur
Publisher: Springer Nature
Published:
Total Pages: 325
ISBN-13: 303151677X
DOWNLOAD EBOOKAn Introduction to Sequential Dynamical Systems
Author: Henning Mortveit
Publisher: Springer Science & Business Media
Published: 2007-11-27
Total Pages: 261
ISBN-13: 0387498796
DOWNLOAD EBOOKThis 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.
Noise, Oscillators and Algebraic Randomness
Author: Michel Planat
Publisher: Springer
Published: 2008-01-11
Total Pages: 417
ISBN-13: 3540454632
DOWNLOAD EBOOKNoise 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.
