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Value Distribution Theory And Complex Dynamics
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Book Synopsis Value Distribution Theory and Complex Dynamics by : Kiyoshi L Igusa
Download or read book Value Distribution Theory and Complex Dynamics written by Kiyoshi L Igusa and published by American Mathematical Soc.. This book was released on 2002 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains six detailed papers written by participants of the special session on value distribution theory and complex dynamics held in Hong Kong at the First Joint International Meeting of the AMS and the Hong Kong Mathematical Society in December 2000. It demonstrates the strong interconnections between the two fields and introduces recent progress of leading researchers from Asia. In the book, W. Bergweiler discusses proper analytic maps with one critical point and generalizes a previous result concerning Leau domains. W. Cherry and J. Wang discuss non-Archimedean analogs of Picard's theorems. P.-C. Hu and C.-C. Yang give a survey of results in non-Archimedean value distribution theory related to unique range sets, the $abc$-conjecture, and Shiffman's conjecture. L. Keen and J. Kotus explore the dynamics of the family of $f_\lambda(z)=\lambda\tan(z)$ and show that it has much in common with the dynamics of the familiar quadratic family $f_c(z)=z^2+c$. R. Oudkerk discusses the interesting phenomenon known as parabolic implosion and, in particular, shows the persistence of Fatou coordinates under perturbation. Finally, M. Taniguchi discusses deformation spaces of entire functions and their combinatorial structure of singularities of the functions. The book is intended for graduate students and research mathematicians interested in complex dynamics, function theory, and non-Archimedean function theory.
Book Synopsis Value Distribution Theory and Related Topics by : Grigor A. Barsegian
Download or read book Value Distribution Theory and Related Topics written by Grigor A. Barsegian and published by Springer Science & Business Media. This book was released on 2006-05-02 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to - alytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal surfaces. Moreover, several appli- tions of the theory have been exploited, including complex differential and functional equations, complex dynamics and Diophantine equations. The main emphasis of this collection is to direct attention to a number of recently developed novel ideas and generalizations that relate to the - velopment of value distribution theory and its applications. In particular, we mean a recent theory that replaces the conventional consideration of counting within a disc by an analysis of their geometric locations. Another such example is presented by the generalizations of the second main theorem to higher dimensional cases by using the jet theory. Moreover, s- ilar ideas apparently may be applied to several related areas as well, such as to partial differential equations and to differential geometry. Indeed, most of these applications go back to the problem of analyzing zeros of certain complex or real functions, meaning in fact to investigate level sets or level surfaces.
Book Synopsis Value Distribution Theory by : L. Sario
Download or read book Value Distribution Theory written by L. Sario and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this research monograph is to build up a modern value distribution theory for complex analytic mappings between abstract Riemann surfaces. All results presented herein are new in that, apart from the classical background material in the last chapter, there is no over lapping with any existing monograph on merom orphic functions. Broadly speaking the division of the book is as follows: The Introduction and Chapters I to III deal mainly with the theory of mappings of arbitrary Riemann surfaces as developed by the first named author; Chapter IV, due to Nakai, is devoted to meromorphic functions on parabolic surfaces; Chapter V contains Matsumoto's results on Picard sets; Chapter VI, pre dominantly due to the second named author, presents the so-called nonintegrated forms of the main theorems and includes some joint work by both authors. For a complete list of writers whose results have been discussed we refer to the Author Index.
Book Synopsis Value Distribution Theory by : Yang Lo
Download or read book Value Distribution Theory written by Yang Lo and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one excep tion. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 A
Book Synopsis Value Distribution Theory Related to Number Theory by : Pei-Chu Hu
Download or read book Value Distribution Theory Related to Number Theory written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2006-10-06 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is Diophantine approximation and Nevanlinna theory. This book proves not just some new results and directions but challenging open problems in Diophantine approximation and Nevanlinna theory. The authors’ newest research activities on these subjects over the past eight years are collected here. Some of the significant findings are the proof of Green-Griffiths conjecture by using meromorphic connections and Jacobian sections, generalized abc-conjecture, and more.
Book Synopsis Geometry, Groups and Dynamics by : C. S. Aravinda
Download or read book Geometry, Groups and Dynamics written by C. S. Aravinda and published by American Mathematical Soc.. This book was released on 2015-05-01 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution.
Book Synopsis Meromorphic Functions over Non-Archimedean Fields by : Pei-Chu Hu
Download or read book Meromorphic Functions over Non-Archimedean Fields written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nevanlinna theory (or value distribution theory) in complex analysis is so beautiful that one would naturally be interested in determining how such a theory would look in the non Archimedean analysis and Diophantine approximations. There are two "main theorems" and defect relations that occupy a central place in N evanlinna theory. They generate a lot of applications in studying uniqueness of meromorphic functions, global solutions of differential equations, dynamics, and so on. In this book, we will introduce non-Archimedean analogues of Nevanlinna theory and its applications. In value distribution theory, the main problem is that given a holomorphic curve f : C -+ M into a projective variety M of dimension n and a family 01 of hypersurfaces on M, under a proper condition of non-degeneracy on f, find the defect relation. If 01 n is a family of hyperplanes on M = r in general position and if the smallest dimension of linear subspaces containing the image f(C) is k, Cartan conjectured that the bound of defect relation is 2n - k + 1. Generally, if 01 is a family of admissible or normal crossings hypersurfaces, there are respectively Shiffman's conjecture and Griffiths-Lang's conjecture. Here we list the process of this problem: A. Complex analysis: (i) Constant targets: R. Nevanlinna[98] for n = k = 1; H. Cartan [20] for n = k > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman's conjecture partially solved by Hu-Yang [71J; Griffiths-Lang's conjecture (open).
Book Synopsis Proceedings of the Second ISAAC Congress by : Heinrich G.W. Begehr
Download or read book Proceedings of the Second ISAAC Congress written by Heinrich G.W. Begehr and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the Proceedings of the Second ISAAC Congress. ISAAC is the acronym of the International Society for Analysis, its Applications and Computation. The president of ISAAC is Professor Robert P. Gilbert, the second named editor of this book, e-mail: [email protected]. The Congress is world-wide valued so highly that an application for a grant has been selected and this project has been executed with Grant No. 11-56 from *the Commemorative Association for the Japan World Exposition (1970). The finance of the publication of this book is exclusively the said Grant No. 11-56 from *. Thus, a pair of each one copy of two volumes of this book will be sent to all contributors, who registered at the Second ISAAC Congress in Fukuoka, free of charge by the Kluwer Academic Publishers. Analysis is understood here in the broad sense of the word, includ ing differential equations, integral equations, functional analysis, and function theory. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. With this objective, ISAAC organizes international Congresses for the presentation and dis cussion of research on analysis. ISAAC welcomes new members and those interested in joining ISAAC are encouraged to look at the web site http://www .math. udel.edu/ gilbert/isaac/index.html vi and http://www.math.fu-berlin.de/ rd/ ag/isaac/newton/index.html.
Book Synopsis Value Distribution Theory by : Le Yang
Download or read book Value Distribution Theory written by Le Yang and published by Springer. This book was released on 1993 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Value-distribution Theory by : Robert O. Kujala
Download or read book Value-distribution Theory written by Robert O. Kujala and published by . This book was released on 1974 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.
Book Synopsis Progress in Analysis by : Heinrich G. W. Begehr
Download or read book Progress in Analysis written by Heinrich G. W. Begehr and published by World Scientific. This book was released on 2003 with total page 1557 pages. Available in PDF, EPUB and Kindle. Book excerpt: The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
Book Synopsis Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) by : Heinrich G W Begehr
Download or read book Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) written by Heinrich G W Begehr and published by World Scientific. This book was released on 2003-08-04 with total page 1556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
Book Synopsis Complex Manifolds and Hyperbolic Geometry by : Clifford J. Earle
Download or read book Complex Manifolds and Hyperbolic Geometry written by Clifford J. Earle and published by American Mathematical Soc.. This book was released on 2002 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume derives from the second Iberoamerican Congress on Geometry, held in 2001 in Mexico at the Centro de Investigacion en Matematicas A.C., an internationally recognized program of research in pure mathematics. The conference topics were chosen with an eye toward the presentation of new methods, recent results, and the creation of more interconnections between the different research groups working in complex manifolds and hyperbolic geometry. This volume reflects both the unity and the diversity of these subjects. Researchers around the globe have been working on problems concerning Riemann surfaces, as well as a wide scope of other issues: the theory of Teichmuller spaces, theta functions, algebraic geometry and classical function theory. Included here are discussions revolving around questions of geometry that are related in one way or another to functions of a complex variable. There are contributors on Riemann surfaces, hyperbolic geometry, Teichmuller spaces, and quasiconformal maps. Complex geometry has many applications--triangulations of surfaces, combinatorics, ordinary differential equations, complex dynamics, and the geometry of special curves and jacobians, among others. In this book, research mathematicians in complex geometry, hyperbolic geometry and Teichmuller spaces will find a selection of strong papers by international experts.
Book Synopsis Advances in Ultrametric Analysis by : Alain Escassut
Download or read book Advances in Ultrametric Analysis written by Alain Escassut and published by American Mathematical Soc.. This book was released on 2018-03-26 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of -adic series, rational maps on the projective line over , non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, -modules with a convex base, non-compact Trace class operators and Schatten-class operators in -adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean Köthe spaces, -adic Nevanlinna theory and applications, and sub-coordinate representation of -adic functions. Moreover, a paper on the history of -adic analysis with a comparative summary of non-Archimedean fields is presented. Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
Book Synopsis Explorations in Complex and Riemannian Geometry by : John Bland
Download or read book Explorations in Complex and Riemannian Geometry written by John Bland and published by American Mathematical Soc.. This book was released on 2003 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.
Book Synopsis Differentiable and Complex Dynamics of Several Variables by : Pei-Chu Hu
Download or read book Differentiable and Complex Dynamics of Several Variables written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R.
Book Synopsis A History of Complex Dynamics by : Daniel S. Alexander
Download or read book A History of Complex Dynamics written by Daniel S. Alexander and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contemporary study of complex dynamics, which has flourished so much in recent years, is based largely upon work by G. Julia (1918) and P. Fatou (1919/20). The goal of this book is to analyze this work from an historical perspective and show in detail, how it grew out of a corpus regarding the iteration of complex analytic functions. This began with investigations by E. Schröder (1870/71) which he made, when he studied Newton's method. In the 1880's, Gabriel Koenigs fashioned this study into a rigorous body of work and, thereby, influenced a lot the subsequent development. But only, when Fatou and Julia applied set theory as well as Paul Montel's theory of normal families, it was possible to develop a global approach to the iteration of rational maps. This book shows, how this intriguing piece of modern mathematics became reality.
