Progress In Holomorphic Dynamics

Author : Hartje Kriete
Publisher : CRC Press
Page : 204 pages
File Size : 55,8 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 : Bodil Branner,Núria Fagella
Publisher : Cambridge University Press
Page : 433 pages
File Size : 50,7 Mb
Release : 2014-01-23
Category : Mathematics
ISBN : 9781107042919

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Quasiconformal Surgery in Holomorphic Dynamics by Bodil Branner,Núria Fagella Pdf

A comprehensive introduction to quasiconformal surgery in holomorphic dynamics. Contains a wide variety of applications and illustrations.

Author : Mikhail Lyubich,Michael Yampolsky
Publisher : American Mathematical Soc.
Page : 412 pages
File Size : 45,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821871560

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Holomorphic Dynamics and Renormalization by Mikhail Lyubich,Michael Yampolsky Pdf

Schwarzian derivatives and cylinder maps by A. Bonifant and J. Milnor Holomorphic dynamics: Symbolic dynamics and self-similar groups by V. Nekrashevych Are there critical points on the boundaries of mother hedgehogs? by D. K. Childers Finiteness for degenerate polynomials by L. DeMarco Cantor webs in the parameter and dynamical planes of rational maps by R. L. Devaney Simple proofs of uniformization theorems by A. A. Glutsyuk The Yoccoz combinatorial analytic invariant by C. L. Petersen and P. Roesch Bifurcation loci of exponential maps and quadratic polynomials: Local connectivity, triviality of fibers, and density of hyperbolicity by L. Rempe and D. Schleicher Rational and transcendental Newton maps by J. Ruckert Newton's method as a dynamical system: Efficient root finding of polynomials and the Riemann $\zeta$ function by D. Schleicher The external boundary of $M_2$ by V. Timorin Renormalization: Renormalization of vector fields by H. Koch Renormalization of arbitrary weak noises for one-dimensional critical dynamical systems: Summary of results and numerical explorations by O. Diaz-Espinosa and R. de la Llave KAM for the nonlinear Schrodinger equation--A short presentation by H. L. Eliasson and S. B. Kuksin Siegel disks and renormalization fixed points by M. Yampolsky

Author : Michael Ruzhansky,Jens Wirth
Publisher : World Scientific
Page : 668 pages
File Size : 50,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814313162

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Progress in Analysis and Its Applications by Michael Ruzhansky,Jens Wirth Pdf

The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.

Author : Michael Ruzhansky,Jens Wirth
Publisher : World Scientific
Page : 668 pages
File Size : 53,5 Mb
Release : 2010-07-29
Category : Mathematics
ISBN : 9789814464703

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Progress In Analysis And Its Applications - Proceedings Of The 7th International Isaac Congress by Michael Ruzhansky,Jens Wirth Pdf

The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.

Author : Xavier Gomez-Mont,Jose A. Seade,Alberto Verjovski
Publisher : Unknown
Page : 340 pages
File Size : 45,7 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 : Bernold Fiedler
Publisher : Springer Science & Business Media
Page : 820 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642565892

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Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by Bernold Fiedler Pdf

Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

Author : Alberto A. Condori,Elodie Pozzi,William T. Ross,Alan A. Sola
Publisher : American Mathematical Society
Page : 226 pages
File Size : 55,7 Mb
Release : 2024-04-30
Category : Mathematics
ISBN : 9781470472467

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Recent Progress in Function Theory and Operator Theory by Alberto A. Condori,Elodie Pozzi,William T. Ross,Alan A. Sola Pdf

This volume contains the proceedings of the AMS Special Session on Recent Progress in Function Theory and Operator Theory, held virtually on April 6, 2022. Function theory is a classical subject that examines the properties of individual elements in a function space, while operator theory usually deals with concrete operators acting on such spaces or other structured collections of functions. These topics occupy a central position in analysis, with important connections to partial differential equations, spectral theory, approximation theory, and several complex variables. With the aid of certain canonical representations or “models”, the study of general operators can often be reduced to that of the operator of multiplication by one or several independent variables, acting on spaces of analytic functions or compressions of this operator to co-invariant subspaces. In this way, a detailed understanding of operators becomes connected with natural questions concerning analytic functions, such as zero sets, constructions of functions constrained by norms or interpolation, multiplicative structures granted by factorizations in spaces of analytic functions, and so forth. In many cases, non-obvious problems initially motivated by operator-theoretic considerations turn out to be interesting on their own, leading to unexpected challenges in function theory. The research papers in this volume deal with the interplay between function theory and operator theory and the way in which they influence each other.

Author : Sergio Albeverio,Franco Flandoli,Yakov G. Sinai
Publisher : Springer
Page : 174 pages
File Size : 46,9 Mb
Release : 2008-04-01
Category : Mathematics
ISBN : 9783540784937

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SPDE in Hydrodynamics: Recent Progress and Prospects by Sergio Albeverio,Franco Flandoli,Yakov G. Sinai Pdf

Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.

Author : John Roe
Publisher : CRC Press
Page : 209 pages
File Size : 41,6 Mb
Release : 2013-12-19
Category : Mathematics
ISBN : 9781482247831

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Elliptic Operators, Topology, and Asymptotic Methods, Second Edition by John Roe Pdf

Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics addressed include Hodge theory, Weyl's theorem on the distribution of the eigenvalues of the Laplacian, the asymptotic expansion for the heat kernel, and the index theorem for Dirac-type operators using Getzler's direct method. As a "dessert," the final two chapters offer discussion of Witten's analytic approach to the Morse inequalities and the L2-index theorem of Atiyah for Galois coverings. The text assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, Elliptic Operators, Topology, and Asymptotic Methods becomes the ideal vehicle for self-study or coursework. Mathematicians, researchers, and physicists working with index theory or supersymmetry will find it a concise but wide-ranging introduction to this important and intriguing field.

Author : Heinrich G. W. Begehr,Robert Pertsch Gilbert,Man Wah Wong
Publisher : World Scientific
Page : 1557 pages
File Size : 43,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812385727

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Progress in Analysis by Heinrich G. W. Begehr,Robert Pertsch Gilbert,Man Wah Wong Pdf

The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.

Author : Robert L. Devaney
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 46,6 Mb
Release : 2006
Category : Domains of holomorphy
ISBN : 9780821836255

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Complex Dynamics by Robert L. Devaney Pdf

Chaotic behavior of (even the simplest) iterations of polynomial maps of the complex plane was known for almost one hundred years due to the pioneering work of Farou, Julia, and their contemporaries. However, it was only twenty-five years ago that the first computer generated images illustrating properties of iterations of quadratic maps appeared. These images of the so-called Mandelbrot and Julia sets immediately resulted in a strong resurgence of interest in complex dynamics. The present volume, based on the talks at the conference commemorating the twenty-fifth anniversary of the appearance of Mandelbrot sets, provides a panorama of current research in this truly fascinating area of mathematics.

Author : S. Morosawa
Publisher : Cambridge University Press
Page : 354 pages
File Size : 53,7 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 : Marco Abate
Publisher : Walter de Gruyter GmbH & Co KG
Page : 372 pages
File Size : 45,7 Mb
Release : 2022-12-05
Category : Mathematics
ISBN : 9783110601978

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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 : Heinrich G W Begehr,Man-wah Wong,Robert Pertsch Gilbert
Publisher : World Scientific
Page : 1556 pages
File Size : 48,8 Mb
Release : 2003-08-04
Category : Mathematics
ISBN : 9789814485234

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Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) by Heinrich G W Begehr,Man-wah Wong,Robert Pertsch Gilbert Pdf

The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.