Holomorphic Dynamical Systems

Author : Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate
Publisher : Springer
Page : 348 pages
File Size : 42,6 Mb
Release : 2010-07-20
Category : Mathematics
ISBN : 9783642131714

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Holomorphic Dynamical Systems by Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate Pdf

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.

Author : Xavier Gomez-Mont,Jose A. Seade,Alberto Verjovski
Publisher : Springer
Page : 335 pages
File Size : 54,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540459576

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Holomorphic Dynamics by Xavier Gomez-Mont,Jose A. Seade,Alberto Verjovski Pdf

The objective of the meeting was to have together leading specialists in the field of Holomorphic Dynamical Systems in order to present their current reseach in the field. The scope was to cover iteration theory of holomorphic mappings (i.e. rational maps), holomorphic differential equations and foliations. Many of the conferences and articles included in the volume contain open problems of current interest. The volume contains only research articles.

Author : S. Morosawa
Publisher : Cambridge University Press
Page : 354 pages
File Size : 47,7 Mb
Release : 2000-01-13
Category : Mathematics
ISBN : 0521662583

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Holomorphic Dynamics by S. Morosawa Pdf

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.

Author : Michel Zinsmeister
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 45,7 Mb
Release : 2000
Category : Mathematics
ISBN : 0821819488

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Thermodynamic Formalism and Holomorphic Dynamical Systems by Michel Zinsmeister Pdf

The purpose of thermodynamics and statistical physics is to understand the equilibrium of a gas or the different states of matter. To understand the strange fractal sets appearing when one iterates a quadratic polynomial is one of the goals of the theory of holomorphic dynamical systems. These two theories are strongly linked: The laws of thermodynamics happen to be an extremely powerful tool for understanding the objects of holomorphic dynamical systems. A "thermodynamic formalism" has been developed, bringing together notions that are a priori unrelated. While the deep reasons of this parallelism remain unknown, the goal of this book is to describe this formalism both from the physical and mathematical point of view in order to understand how it works and how useful it can be. This translation is a slightly revised version of the original French edition. The main changes are in Chapters 5 and 6 and consist of clarification of some proofs and a new presentation of the basics in iteration of polynomials.

Author : Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 45,8 Mb
Release : 2010-07-31
Category : Mathematics
ISBN : 9783642131707

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Holomorphic Dynamical Systems by Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate Pdf

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.

Author : Christoph List
Publisher : Unknown
Page : 137 pages
File Size : 40,8 Mb
Release : 2005
Category : Differentiable dynamical systems
ISBN : 0954426924

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Linearization of Holomorphic Dynamical Systems by Christoph List Pdf

Author : Mikhail Lyubich,Michael Yampolsky
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 42,9 Mb
Release : 2008
Category : Hamiltonian systems
ISBN : 9780821842751

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Holomorphic Dynamics and Renormalization by Mikhail Lyubich,Michael Yampolsky Pdf

Collects papers that reflect some of the directions of research in two closely related fields: Complex Dynamics and Renormalization in Dynamical Systems. This title contains papers that introduces the reader to this fascinating world and a related area of transcendental dynamics. It also includes open problems and computer simulations.

Author : Hartje Kriete
Publisher : CRC Press
Page : 204 pages
File Size : 53,8 Mb
Release : 1998-05-20
Category : Mathematics
ISBN : 0582323886

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Progress in Holomorphic Dynamics by Hartje Kriete Pdf

In the last few decades, complex dynamical systems have received widespread public attention and emerged as one of the most active fields of mathematical research. Starting where other monographs in the subject end, Progress in Holomorphic Dynamics advances the theoretical aspects and recent results in complex dynamical systems, with particular emphasis on Siegel discs. Organized into four parts, the papers in this volume grew out of three workshops: two hosted by the Georg-August-Universität Göttingen and one at the "Mathematisches Forschungsinstitut Oberwolfach." Part I addresses linearization. The authors review Yoccoz's proof that the Brjuno condition is the optimal condition for linearizability of indifferent fixed points and offer a treatment of Perez-Marco's refinement of Yoccoz's work. Part II discusses the conditions necessary for the boundary of a Siegel disc to contain a critical point, builds upon Herman's work, and offers a survey of the state-of-the-art regarding the boundaries of Siegel discs. Part III deals with the topology of Julia sets with Siegel discs and contains a remarkable highlight: C.L. Petersen establishes the existence of Siegel discs of quadratic polynomials with a locally connected boundary. Keller, taking a different approach, explains the relations between locally connected "real Julia sets" with Siegel discs and the abstract concepts of kneading sequences and itineraries. Part IV closes the volume with four papers that review the different directions of present research in iteration theory. It includes discussions on the relations between commuting rational functions and their Julia sets, interactions between the iteration of polynomials and the iteration theory of entire transcendental functions, a deep analysis of the topology of the limbs of the Mandelbrot set, and an overview of complex dynamics in higher dimensions.

Author : Xavier Gomez-Mont,Jose A. Seade,Alberto Verjovski
Publisher : Unknown
Page : 340 pages
File Size : 48,9 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662207753

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Holomorphic Dynamics by Xavier Gomez-Mont,Jose A. Seade,Alberto Verjovski Pdf

Author : Dominique Cerveau
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 50,6 Mb
Release : 2003
Category : Mathematics
ISBN : 082183228X

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Complex Dynamics and Geometry by Dominique Cerveau Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 159 pages
File Size : 41,9 Mb
Release : 1996
Category : Electronic
ISBN : OCLC:39305515

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Topology of Holomorphic Dynamical Systems and Related Topics by Anonim Pdf

Author : Marco Abate
Publisher : Walter de Gruyter GmbH & Co KG
Page : 2706 pages
File Size : 49,6 Mb
Release : 2022-12-05
Category : Mathematics
ISBN : 9783110598742

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Holomorphic Dynamics on Hyperbolic Riemann Surfaces by Marco Abate Pdf

This completely revised and updated edition of the one variable part of the author's classic older book "Iteration Theory of Holomorphic Maps on Taut Manifolds" presents the theory of holomorphic dynamical systems on hyperbolic Riemann surfaces from the very beginning of the subject up to the most recent developments. It is intended both as a reference book for the experts and as an accessible gateway to this beautiful theory for Master and Ph.D. students. It also contains extensive historical notes and references for further readings.

Author : John Milnor
Publisher : Princeton University Press
Page : 313 pages
File Size : 46,6 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9781400835539

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Dynamics in One Complex Variable. (AM-160) by John Milnor Pdf

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 : Albert Fathi,J.-C. Yoccoz
Publisher : Cambridge University Press
Page : 597 pages
File Size : 43,5 Mb
Release : 2006-02-02
Category : Mathematics
ISBN : 9780521860680

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Dynamical Systems by Albert Fathi,J.-C. Yoccoz Pdf

A collection of up-to-date research and classic papers reflecting the work of Michael Herman.

Author : Mark Agranovsky,Anatoly Golberg,Fiana Jacobzon,David Shoikhet,Lawrence Zalcman
Publisher : Birkhäuser
Page : 372 pages
File Size : 41,9 Mb
Release : 2018-01-31
Category : Mathematics
ISBN : 9783319701547

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Complex Analysis and Dynamical Systems by Mark Agranovsky,Anatoly Golberg,Fiana Jacobzon,David Shoikhet,Lawrence Zalcman Pdf

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.