Differentiable And Complex Dynamics Of Several Variables

Author : Pei-Chu Hu
Publisher : Springer Science & Business Media
ISBN 13 : 9401592993
Total Pages : 348 pages
Book Rating : 4.94/5 ( download)

DOWNLOAD NOW!

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.

Author : Pei-Chu Hu
Publisher :
ISBN 13 : 9789401593007
Total Pages : 352 pages
Book Rating : 4.00/5 ( download)

DOWNLOAD NOW!

Download or read book Differentiable and Complex Dynamics of Several Variables written by Pei-Chu Hu and published by . This book was released on 2014-01-15 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : John Milnor
Publisher : Princeton University Press
ISBN 13 : 1400835534
Total Pages : 313 pages
Book Rating : 4.39/5 ( download)

DOWNLOAD NOW!

Download or read book Dynamics in One Complex Variable. (AM-160) 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.

Author : Daniel S. Alexander
Publisher : American Mathematical Soc.
ISBN 13 : 0821844644
Total Pages : 474 pages
Book Rating : 4.49/5 ( download)

DOWNLOAD NOW!

Download or read book Early Days in Complex Dynamics written by Daniel S. Alexander and published by American Mathematical Soc.. This book was released on 2012 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others.

Author : Pei-Chu Hu
Publisher : Springer Science & Business Media
ISBN 13 : 9401594155
Total Pages : 296 pages
Book Rating : 4.58/5 ( download)

DOWNLOAD NOW!

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).

Author : Themistocles M. Rassias
Publisher : Springer
ISBN 13 : 1493911066
Total Pages : 783 pages
Book Rating : 4.66/5 ( download)

DOWNLOAD NOW!

Download or read book Mathematics Without Boundaries written by Themistocles M. Rassias and published by Springer. This book was released on 2014-09-17 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.

Author : Sergeĭ Mikhaĭlovich Nikolʹskiĭ
Publisher : American Mathematical Soc.
ISBN 13 : 9780821830833
Total Pages : 264 pages
Book Rating : 4.3X/5 ( download)

DOWNLOAD NOW!

Download or read book Theory and Applications of Differentiable Functions of Several Variables written by Sergeĭ Mikhaĭlovich Nikolʹskiĭ and published by American Mathematical Soc.. This book was released on 1984 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : So-chin Chen
Publisher : American Mathematical Society(RI)
ISBN 13 : 9780821810620
Total Pages : 0 pages
Book Rating : 4.26/5 ( download)

DOWNLOAD NOW!

Download or read book Partial Differential Equations in Several Complex Variables written by So-chin Chen and published by American Mathematical Society(RI). This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations.

Author : H Begehr
Publisher : Chapman and Hall/CRC
ISBN 13 : 9780582255005
Total Pages : 464 pages
Book Rating : 4.07/5 ( download)

DOWNLOAD NOW!

Download or read book An Introduction to Several Complex Variables and Partial Differential Equations written by H Begehr and published by Chapman and Hall/CRC. This book was released on 1997-07-09 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : John Erik Fornæss
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889312
Total Pages : 74 pages
Book Rating : 4.11/5 ( download)

DOWNLOAD NOW!

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 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is part of the 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. These notes provide an easy to read introduction into the field. This monograph then points readers towards technically more advanced literature.