Holomorphic Dynamical Systems
Holomorphic Dynamical Systems

Author: Nessim Sibony

Publisher: Springer Science & Business Media

Published: 2010-07-31

Total Pages: 357

ISBN-13: 3642131700

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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.

Asymptotics and Borel Summability
Asymptotics and Borel Summability

Author: Ovidiu Costin

Publisher: CRC Press

Published: 2008-12-04

Total Pages: 266

ISBN-13: 1420070320

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Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, tr

Value Distribution of Meromorphic Functions
Value Distribution of Meromorphic Functions

Author: Anatoliĭ Asirovich Golʹdberg

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 488

ISBN-13: 9780821842652

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"This book contains a comprehensive exposition of the Nevanlinna theory of meromorphic functions of one complex variable, with detailed study of deficiencies, value distribution, and asymptotic properties of meromorphic functions." "The main body of the book is a translation of the Russian original published in 1970, which has been one of the most popular sources in this field since then. New references and footnotes related to recent achievements in the topics considered in the original edition have been added and a few corrections made. A new Appendix with a survey of the results obtained after 1970 and extensive bibliography has been written by Alexandre Ermenko and James K. Langley for this English edition." "The only prerequisite for understanding material of this book is an undergraduate course in the theory of functions of one complex variable."--BOOK JACKET.

Finite Blaschke Products and Their Connections
Finite Blaschke Products and Their Connections

Author: Stephan Ramon Garcia

Publisher: Springer

Published: 2018-05-24

Total Pages: 340

ISBN-13: 3319782479

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This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products. In addition, model spaces, rational functions with real boundary values, spectral mapping properties of the numerical range, and the Darlington synthesis problem from electrical engineering are also covered. Topics are carefully discussed, and numerous examples and illustrations highlight crucial ideas. While thorough explanations allow the reader to appreciate the beauty of the subject, relevant exercises following each chapter improve technical fluency with the material. With much of the material previously scattered throughout mathematical history, this book presents a cohesive, comprehensive and modern exposition accessible to undergraduate students, graduate students, and researchers who have familiarity with complex analysis.

American Journal of Mathematics
American Journal of Mathematics

Author:

Publisher:

Published: 1941

Total Pages: 918

ISBN-13:

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The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.