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Lectures On Fractal Geometry And Dynamical Systems
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Book Synopsis Lectures on Fractal Geometry and Dynamical Systems by : Ya. B. Pesin
Download or read book Lectures on Fractal Geometry and Dynamical Systems written by Ya. B. Pesin and published by American Mathematical Soc.. This book was released on 2009 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. This book offers an introduction to these two fields, with an emphasis on the relationship between them.
Book Synopsis Lectures On Fractal Geometry by : Martina Zaehle
Download or read book Lectures On Fractal Geometry written by Martina Zaehle and published by World Scientific. This book was released on 2023-12-27 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a series of lectures at the Mathematics Department of the University of Jena, developed in the period from 1995 up to 2015. It is completed by additional material and extensions of some basic results from the literature to more general metric spaces.This book provides a clear introduction to classical fields of fractal geometry, which provide some background for modern topics of research and applications. Some basic knowledge on general measure theory and on topological notions in metric spaces is presumed.
Book Synopsis Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II by : Benoit B. Mandelbrot
Download or read book Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II written by Benoit B. Mandelbrot and published by . This book was released on 2013 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II by : David Carfi
Download or read book Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II written by David Carfi and published by American Mathematical Soc.. This book was released on 2013-10-24 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.
Book Synopsis Chaos and Fractals: The Mathematics Behind the Computer Graphics by : Robert L. Devaney
Download or read book Chaos and Fractals: The Mathematics Behind the Computer Graphics written by Robert L. Devaney and published by American Mathematical Soc.. This book was released on 1989 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Robert Devaney communicates his deep understanding as well as his enthusiasm for chaos, fractals, and dynamical systems. Starting at a level suitable for well-prepared high school students, he tells the mathematical story behind these fascinating topics. Equations and graphs are clearly shown with computer-generated characters, and Devaney's explanations are lucid and instructive. Illustrating the mathematics are forays into the colorful, unpredictable world of fractals and Julia sets. Devaney explains how the computer is used to generate the pictures and shows how the various colors are chosen for graphical representations ... Though the mathematical background required is elementary, those at the collegiate level and beyond will appreciate ... the clarity of exposition and the sheer beauty of the graphics."--Container.
Book Synopsis Recent Developments in Fractal Geometry and Dynamical Systems by : Sangita Jha
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.
Book Synopsis The Beauty of Fractals by : Heinz-Otto Peitgen
Download or read book The Beauty of Fractals written by Heinz-Otto Peitgen and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now approaching its tenth year, this hugely successful book presents an unusual attempt to publicise the field of Complex Dynamics. The text was originally conceived as a supplemented catalogue to the exhibition "Frontiers of Chaos", seen in Europe and the United States, and describes the context and meaning of these fascinating images. A total of 184 illustrations - including 88 full-colour pictures of Julia sets - are suggestive of a coffee-table book. However, the invited contributions which round off the book lend the text the required formality. Benoit Mandelbrot gives a very personal account, in his idiosyncratic self-centred style, of his discovery of the fractals named after him and Adrien Douady explains the solved and unsolved problems relating to this amusingly complex set.
Book Synopsis Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot by : Michel Laurent Lapidus
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 534 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.
Book Synopsis Chaotic Dynamics and Fractals by : Michael F. Barnsley
Download or read book Chaotic Dynamics and Fractals written by Michael F. Barnsley and published by Academic Press. This book was released on 2014-05-10 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaotic Dynamics and Fractals covers the proceedings of the 1985 Conference on Chaotic Dynamics, held at the Georgia Institute of Technology. This conference deals with the research area of chaos, dynamical systems, and fractal geometry. This text is organized into three parts encompassing 16 chapters. The first part describes the nature of chaos and fractals, the geometric tool for some strange attractors, and other complicated sets of data associated with chaotic systems. This part also considers the Henon-Hiles Hamiltonian with complex time, a Henon family of maps from C2 into itself, and the idea of turbulent maps in the course of presenting results on iteration of continuous maps from the unit interval to itself. The second part discusses complex analytic dynamics and associated fractal geometry, specifically the bursts into chaos, algorithms for obtaining geometrical and combinatorial information, and the parameter space for iterated cubic polynomials. This part also examines the differentiation of Julia sets with respects to a parameter in the associated rational map, permitting the formulation of Taylor series expansion for the sets. The third part highlights the applications of chaotic dynamics and fractals. This book will prove useful to mathematicians, physicists, and other scientists working in, or introducing themselves to, the field.
Book Synopsis Dynamics with Chaos and Fractals by : Marat Akhmet
Download or read book Dynamics with Chaos and Fractals written by Marat Akhmet and published by Springer Nature. This book was released on 2020-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.
Book Synopsis Fractal Geometry and Analysis by : Jacques Bélair
Download or read book Fractal Geometry and Analysis written by Jacques Bélair and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Universite de Montreal - was devoted to Fractal Geometry and Analysis. The present volume is the fruit of the work of this Advanced Study Institute. We were fortunate to have with us Prof. Benoit Mandelbrot - the creator of numerous concepts in Fractal Geometry - who gave a series of lectures on multifractals, iteration of analytic functions, and various kinds of fractal stochastic processes. Different foundational contributions for Fractal Geometry like measure theory, dy namical systems, iteration theory, branching processes are recognized. The geometry of fractal sets and the analytical tools used to investigate them provide a unifying theme of this book. The main topics that are covered are then as follows. Dimension Theory. Many definitions of fractional dimension have been proposed, all of which coincide on "regular" objects, but often take different values for a given fractal set. There is ample discussion on piecewise estimates yielding actual values for the most common dimensions (Hausdorff, box-counting and packing dimensions). The dimension theory is mainly discussed by Mendes-France, Bedford, Falconer, Tricot and Rata. Construction of fractal sets. Scale in variance is a fundamental property of fractal sets.
Book Synopsis Ergodic Theory and Fractal Geometry by : Hillel Furstenberg
Download or read book Ergodic Theory and Fractal Geometry written by Hillel Furstenberg and published by . This book was released on 2017-06-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: fractal Geometry represents a radical departure from classical Geometry, which focuses on smooth objects that straighten out under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as zooming in. this zooming-in process has its parallels in dynamics, and the varying scenery corresponds to the evolution of dynamical variables. the present monograph focuses on applications of one branch of dynamics ergodic theory the Geometry of fractals. Much attention is given to the all-important notion of Fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of Fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics.
Book Synopsis Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets by : Robert L. Devaney
Download or read book Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets written by Robert L. Devaney and published by American Mathematical Soc.. This book was released on 1994 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mandelbrot set has emerged as one of the most recognizable objects in mathematics. While there is no question of its beauty, relatively few people appreciate the fact that the mathematics behind such images is equally beautiful. This book presents lectures delivered during the AMS Short Course entitled Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets, held at the Joint Mathematics Meetings in Cincinnati in January 1994. The lectures cover a wide range of topics, including the classical work of Julia and Fatou on local dynamics of analytic maps as well as recent work on the dynamics of quadratic and cubic polynomials, the geometry of Julia sets, and the structure of various parameter spaces. Among the other topics are recent results on Yoccoz puzzles and tableaux, limiting dynamics near parabolic points, the spider algorithm, extensions of the theory to rational maps, Newton's method, and entire transcendental functions. Much of the book is accessible to anyone with a background in the basics of dynamical systems and complex analysis.
Book Synopsis Ergodic Theory and Fractal Geometry by : Hillel Furstenberg
Download or read book Ergodic Theory and Fractal Geometry written by Hillel Furstenberg and published by American Mathematical Society. This book was released on 2014-08-08 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry represents a radical departure from classical geometry, which focuses on smooth objects that "straighten out" under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as "zooming in". This zooming-in process has its parallels in dynamics, and the varying "scenery" corresponds to the evolution of dynamical variables. The present monograph focuses on applications of one branch of dynamics--ergodic theory--to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics. A co-publication of the AMS and CBMS.
Book Synopsis Fractal Geometry and Stochastics II by : Christoph Bandt
Download or read book Fractal Geometry and Stochastics II written by Christoph Bandt and published by Birkhäuser. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of contributions by outstanding mathematicians, highlighting the principal directions of research on the combination of fractal geometry and stochastic methods. Clear expositions introduce the most recent results and problems on these subjects and give an overview of their historical development.
Book Synopsis Discrete Dynamical Systems, Chaos Theory and Fractals by : Linda Sundbye
Download or read book Discrete Dynamical Systems, Chaos Theory and Fractals written by Linda Sundbye and published by Createspace Independent Publishing Platform. This book was released on 2018-10-05 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory undergraduate level text on chaos theory, nonlinear dynamics and fractal geometry.
Book Synopsis Fractal Geometry by : Kenneth Falconer
Download or read book Fractal Geometry written by Kenneth Falconer and published by John Wiley & Sons. This book was released on 2004-01-09 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition. * Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals. * Each topic is carefully explained and illustrated by examples and figures. * Includes all necessary mathematical background material. * Includes notes and references to enable the reader to pursue individual topics. * Features a wide selection of exercises, enabling the reader to develop their understanding of the theory. * Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers. Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences. Also by Kenneth Falconer and available from Wiley: Techniques in Fractal Geometry ISBN 0-471-95724-0
