Dynamics in One Complex Variable. (AM-160)

Dynamics in One Complex Variable. (AM-160) PDF

Author: John Milnor

Publisher: Princeton University Press

Published: 2011-02-11

Total Pages: 313

ISBN-13: 1400835534

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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.

Dynamics in One Complex Variable. (AM-160), 3rd Edition

Dynamics in One Complex Variable. (AM-160), 3rd Edition PDF

Author: John Milnor

Publisher:

Published: 2011

Total Pages: 320

ISBN-13:

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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.

Dynamics in One Complex Variable

Dynamics in One Complex Variable PDF

Author: John Milnor

Publisher: Vieweg+teubner Verlag

Published: 2000-06-28

Total Pages: 278

ISBN-13:

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This text 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. The subject is large and rapidly growing. These notes are intended to introduce the reader to 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.

Advances in Iterative Methods for Nonlinear Equations

Advances in Iterative Methods for Nonlinear Equations PDF

Author: Sergio Amat

Publisher: Springer

Published: 2016-09-27

Total Pages: 286

ISBN-13: 331939228X

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This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations, and their approximation.

Metric Spaces of Non-Positive Curvature

Metric Spaces of Non-Positive Curvature PDF

Author: Martin R. Bridson

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 665

ISBN-13: 3662124947

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A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.

Dynamics in Several Complex Variables

Dynamics in Several Complex Variables PDF

Author: John Erik Fornæss

Publisher: American Mathematical Soc.

Published:

Total Pages: 74

ISBN-13: 9780821889312

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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.

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