Download or read book Random Iteration of Rational Functions written by David Simmons and published by . This book was released on 2012 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Iteration of Rational Functions written by Simmons David and published by LAP Lambert Academic Publishing. This book was released on 2014-01 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to study the ergodic theory of holomorphic random dynamical systems on the Riemann sphere. Specifically, the main results are two generalizations of a theorem of Denker and Urba ski ('91) concerning existence and uniqueness of equilibrium states of rational functions with respect to Holder continuous potential functions satisfying a "pressure gap" condition. The main results also generalize a theorem of Jonsson ('00).
Download or read book Random Iterations of Rational Functions written by John Erik Fornaess and published by . This book was released on 1990 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iteration of Rational Functions written by Alan F. Beardon and published by Springer Science & Business Media. This book was released on 2000-09-27 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on complex analytic dynamics, which dates from 1916 and is currently attracting considerable interest. The text provides a comprehensive, well-organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The coverage extends from early memoirs of Fatou and Julia to important recent results and methods of Sullivan and Shishikura. Many details of the proofs have not appeared in print before.
Download or read book Fractal Geometry and Applications A Jubilee of Benoit Mandelbrot written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2004 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
Download or read book Selected Papers on Analysis and Differential Equations written by American Mathematical Society and published by American Mathematical Soc.. This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume includes English translation of ten expository articles published in the Japanese journal Sugaku."
Download or read book Recent Developments in Fractal Geometry and Dynamical Systems written by Sangita Jha and published by American Mathematical Society. This book was released on 2024-04-18 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual AMS Special Session on Fractal Geometry and Dynamical Systems, held from May 14–15, 2022. The content covers a wide range of topics. It includes nonautonomous dynamics of complex polynomials, theory and applications of polymorphisms, topological and geometric problems related to dynamical systems, and also covers fractal dimensions, including the Hausdorff dimension of fractal interpolation functions. Furthermore, the book contains a discussion of self-similar measures as well as the theory of IFS measures associated with Bratteli diagrams. This book is suitable for graduate students interested in fractal theory, researchers interested in fractal geometry and dynamical systems, and anyone interested in the application of fractals in science and engineering. This book also offers a valuable resource for researchers working on applications of fractals in different fields.
Download or read book On the Iteration of Rational Functions written by Joseph Fels Ritt and published by . This book was released on 1920* with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Distance Expanding Random Mappings Thermodynamical Formalism Gibbs Measures and Fractal Geometry written by Volker Mayer and published by Springer Science & Business Media. This book was released on 2011-10-26 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of random dynamical systems originated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many properties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets.
Download or read book The Iteration of Rational Functions and Their Julian Sets written by Chrystina M. Howard and published by . This book was released on 1994 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorics and Finite Fields written by Kai-Uwe Schmidt and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.
Download or read book Thirty Years After Sharkovskii s Theorem New Perspectives Proceedings Of The Conference written by Luis Alseda and published by World Scientific. This book was released on 1996-01-23 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain a collection of papers on Combinatorial Dynamics, from the lectures that took place during the international symposium, Thirty Years after Sharkovskiĭ's Theorem: New Perspectives, which was held at La Manga del Mar Menor, Murcia, Spain, from June 13 to June 18, 1994.Since Professor A N Sharkovskiĭ's landmark paper on the coexistence of periods for interval maps, several lines of research have been developed, opening applications of models to help understand a number of phenomena from a wide variety of fields, such as biology, economics, physics, etc. The meeting served to summarize the progress made since Professor Sharkovskiĭ's discovery, and to explore new directions.
Download or read book Real Methods in Complex and CR Geometry written by John Erik Fornaess and published by Springer Science & Business Media. This book was released on 2004 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of mathematics of Kyoto University written by Kyōto Daigaku and published by . This book was released on 1961 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Download or read book Operator Theory And Analysis Of Infinite Networks written by Palle Jorgensen and published by World Scientific. This book was released on 2023-03-21 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains.The present volume takes the nonstandard approach of analyzing resistance networks from the point of view of Hilbert space theory, where the inner product is defined in terms of Dirichlet energy. The resulting viewpoint emphasizes orthogonality over convexity and provides new insights into the connections between harmonic functions, operators, and boundary theory. Novel applications to mathematical physics are given, especially in regard to the question of self-adjointness of unbounded operators.New topics are covered in a host of areas accessible to multiple audiences, at both beginning and more advanced levels. This is accomplished by directly linking diverse applied questions to such key areas of mathematics as functional analysis, operator theory, harmonic analysis, optimization, approximation theory, and probability theory.
Download or read book Dynamical Systems written by I?Akov Grigor?evich Sina? and published by World Scientific. This book was released on 1991 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of very high quality articles which not only give a very good account of this field in the Soviet Union, but also provide stimulating materials for researchers working on this topic.
