Download or read book Dynamics in Several Complex Variables written by John Erik Fornæss and published by American Mathematical Soc.. This book was released on 1996 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This CBMS lecture series, held in Albany, New York in June 1994 aimed to introduce the audience to the literature on complex dynamics in higher dimension. Some of the lectures are updated versions of earlier lectures given jointly with Nessim Sibony in Montreal 1993. the authro's intent in this book is to give an expansion of the Montreal lectures, basing complex dynamics in higher dimension systematically on pluripotential theory.
Download or read book Dynamics in One Complex Variable written by John Milnor and published by Princeton University Press. This book was released on 2011-02-11 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.
Download or read book Complex Dynamics written by Lennart Carleson and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. Focusing on the analytic side of this contemporary subject, the text was developed from a course taught over several semesters and aims to help students and instructors to familiarize themselves with complex dynamics. Topics covered include: conformal and quasi-conformal mappings, fixed points and conjugations, basic rational iteration, classification of periodic components, critical points and expanding maps, some applications of conformal mappings, the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set.
Download or read book Holomorphic Dynamical Systems written by Nessim Sibony and published by Springer Science & Business Media. This book was released on 2010-07-31 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.
Download or read book Holomorphic Dynamics written by S. Morosawa and published by Cambridge University Press. This book was released on 2000-01-13 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2000, is a comprehensive introduction to holomorphic dynamics, that is the dynamics induced by the iteration of various analytic maps in complex number spaces. This has been the focus of much attention in recent years, with, for example, the discovery of the Mandelbrot set, and work on chaotic behaviour of quadratic maps. The treatment is mathematically unified, emphasizing the substantial role played by classical complex analysis in understanding holomorphic dynamics as well as giving an up-to-date coverage of the modern theory. The authors cover entire functions, Kleinian groups and polynomial automorphisms of several complex variables such as complex Henon maps, as well as the case of rational functions. The book will be welcomed by graduate students and professionals in pure mathematics and science who seek a reasonably self-contained introduction to this exciting area.
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.
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.
Download or read book Algebraic and Geometric Dynamics in Several Complex Variables written by Marius V. Dabija and published by . This book was released on 2000 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elementary Theory of Analytic Functions of One or Several Complex Variables written by Henri Cartan and published by Courier Corporation. This book was released on 2013-04-22 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
Download or read book Complex Algebraic Foliations written by Alcides Lins Neto and published by de Gruyter. This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a basic reference in the modern theory of holomorphic foliations, presenting the interplay between various aspects of the theory and utilizing methods from algebraic and complex geometry along with techniques from complex dynamics and s
Download or read book Introduction to Complex Variables and Applications written by Mark J. Ablowitz and published by Cambridge University Press. This book was released on 2021-03-25 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.
Download or read book Frontiers in Complex Dynamics written by Araceli Bonifant and published by Princeton University Press. This book was released on 2014-03-16 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky.
Download or read book Quasiconformal Surgery in Holomorphic Dynamics written by Bodil Branner and published by Cambridge University Press. This book was released on 2014-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to quasiconformal surgery in holomorphic dynamics. Contains a wide variety of applications and illustrations.
Download or read book Advancements in Complex Analysis written by Daniel Breaz and published by Springer Nature. This book was released on 2020-05-12 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions to this volume are devoted to a discussion of state-of-the-art research and treatment of problems of a wide spectrum of areas in complex analysis ranging from pure to applied and interdisciplinary mathematical research. Topics covered include: holomorphic approximation, hypercomplex analysis, special functions of complex variables, automorphic groups, zeros of the Riemann zeta function, Gaussian multiplicative chaos, non-constant frequency decompositions, minimal kernels, one-component inner functions, power moment problems, complex dynamics, biholomorphic cryptosystems, fermionic and bosonic operators. The book will appeal to graduate students and research mathematicians as well as to physicists, engineers, and scientists, whose work is related to the topics covered.
Download or read book Metrical and Dynamical Aspects in Complex Analysis written by Léa Blanc-Centi and published by Springer. This book was released on 2017-11-03 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in the fields of several complex variables and metric geometry. The different topics are treated coherently and include expository presentations of the relevant tools, techniques and objects, which will be particularly useful for graduate and PhD students specializing in the area.
Download or read book Complex Dynamics and Geometry written by Dominique Cerveau and published by American Mathematical Soc.. This book was released on 2003 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last twenty years, the theory of holomorphic dynamical systems has had a resurgence of activity, particularly concerning the fine analysis of Julia sets associated with polynomials and rational maps in one complex variable. At the same time, closely related theories have had a similar rapid development, for example the qualitative theory of differential equations in the complex domain. The meeting, ``Etat de la recherche'', held at Ecole Normale Superieure de Lyon, presented the current state of the art in this area, emphasizing the unity linking the various sub-domains. This volume contains four survey articles corresponding to the talks presented at this meeting. D. Cerveau describes the structure of polynomial differential equations in the complex plane, focusing on the local analysis in neighborhoods of singular points. E. Ghys surveys the theory of laminations by Riemann surfaces which occur in many dynamical or geometrical situations. N. Sibony describes the present state of the generalization of the Fatou-Julia theory for polynomial or rational maps in two or more complex dimensions. Lastly, the talk by J.-C. Yoccoz, written by M. Flexor, considers polynomials of degree $2$ in one complex variable, and in particular, with the hyperbolic properties of these polynomials centered around the Jakobson theorem. This is a general introduction that gives a basic history of holomorphic dynamical systems, demonstrating the numerous and fruitful interactions among the topics. In the spirit of the ``Etat de la recherche de la SMF'' meetings, the articles are written for a broad mathematical audience, especially students or mathematicians working in different fields. This book is translated from the French edition by Leslie Kay.
Download or read book Several Complex Variables written by Michael Schneider and published by Cambridge University Press. This book was released on 1999 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.
