Cycles Of Polynomial Mappings
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Polynomial Mappings
| Author | : Wladyslaw Narkiewicz |
| Publisher | : Springer |
| Total Pages | : 144 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540492666 |
The book deals with certain algebraic and arithmetical questions concerning polynomial mappings in one or several variables. Algebraic properties of the ring Int(R) of polynomials mapping a given ring R into itself are presented in the first part, starting with classical results of Polya, Ostrowski and Skolem. The second part deals with fully invariant sets of polynomial mappings F in one or several variables, i.e. sets X satisfying F(X)=X . This includes in particular a study of cyclic points of such mappings in the case of rings of algebrai integers. The text contains several exercises and a list of open problems.
The Arithmetic and Geometry of Algebraic Cycles
| Author | : B. Brent Gordon |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 652 |
| Release | : 2000-02-29 |
| Genre | : Mathematics |
| ISBN | : 9780792361947 |
The subject of algebraic cycles has thrived through its interaction with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to such developments as a description of Chow groups in terms of algebraic K-theory, the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge and Tate, and the conjectures of Bloch and Beilinson. The immense recent progress in algebraic cycles, based on so many interactions with so many other areas of mathematics, has contributed to a considerable degree of inaccessibility, especially for graduate students. Even specialists in one approach to algebraic cycles may not understand other approaches well. This book offers students and specialists alike a broad perspective of algebraic cycles, presented from several viewpoints, including arithmetic, transcendental, topological, motives and K-theory methods. Topics include a discussion of the arithmetic Abel-Jacobi mapping, higher Abel-Jacobi regulator maps, polylogarithms and L-series, candidate Bloch-Beilinson filtrations, applications of Chern-Simons invariants to algebraic cycles via the study of algebraic vector bundles with algebraic connection, motivic cohomology, Chow groups of singular varieties, and recent progress on the Hodge and Tate conjectures for Abelian varieties.
The Arithmetic of Dynamical Systems
| Author | : J.H. Silverman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 518 |
| Release | : 2010-05-05 |
| Genre | : Mathematics |
| ISBN | : 038769904X |
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.
Topological Types of Polynomial Mappings
| Author | : John D. Randall |
| Publisher | : |
| Total Pages | : 178 |
| Release | : 2020 |
| Genre | : Mappings (Mathematics) |
| ISBN | : |
Algebraic Number Theory and Diophantine Analysis
| Author | : F. Halter-Koch |
| Publisher | : Walter de Gruyter |
| Total Pages | : 573 |
| Release | : 2011-06-24 |
| Genre | : Mathematics |
| ISBN | : 3110801957 |
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Elementary and Analytic Theory of Algebraic Numbers
| Author | : Wladyslaw Narkiewicz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 732 |
| Release | : 2004-06-24 |
| Genre | : Mathematics |
| ISBN | : 9783540219026 |
This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Polynomials and Vanishing Cycles
| Author | : Mihai Tibăr |
| Publisher | : Cambridge University Press |
| Total Pages | : 13 |
| Release | : 2007-05-17 |
| Genre | : Mathematics |
| ISBN | : 1139463640 |
The behaviour of vanishing cycles is the cornerstone for understanding the geometry and topology of families of hypersurfaces, usually regarded as singular fibrations. This self-contained tract proposes a systematic geometro-topological approach to vanishing cycles, especially those appearing in non-proper fibrations, such as the fibration defined by a polynomial function. Topics which have been the object of active research over the past 15 years, such as holomorphic germs, polynomial functions, and Lefschetz pencils on quasi-projective spaces, are here shown in a new light: conceived as aspects of a single theory with vanishing cycles at its core. Throughout the book the author presents the current state of the art. Transparent proofs are provided so that non-specialists can use this book as an introduction, but all researchers and graduate students working in differential and algebraic topology, algebraic geometry, and singularity theory will find this book of great use.
Applied Algebraic Dynamics
| Author | : Vladimir Anashin |
| Publisher | : Walter de Gruyter |
| Total Pages | : 558 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 3110203006 |
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets
| Author | : Robert L. Devaney |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 223 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 0821802909 |
The Mandelbrot set has emerged as one of the most recognizable objects in mathematics. While there is no question of its beauty, relatively few people appreciate the fact that the mathematics behind such images is equally beautiful. This book presents lectures delivered during the AMS Short Course entitled Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets, held at the Joint Mathematics Meetings in Cincinnati in January 1994. The lectures cover a wide range of topics, including the classical work of Julia and Fatou on local dynamics of analytic maps as well as recent work on the dynamics of quadratic and cubic polynomials, the geometry of Julia sets, and the structure of various parameter spaces. Among the other topics are recent results on Yoccoz puzzles and tableaux, limiting dynamics near parabolic points, the spider algorithm, extensions of the theory to rational maps, Newton's method, and entire transcendental functions. Much of the book is accessible to anyone with a background in the basics of dynamical systems and complex analysis.
