Recent Developments In Fractal Geometry And Dynamical Systems

Author : Julien Barral,Stéphane Seuret
Publisher : Birkhäuser
Page : 312 pages
File Size : 40,5 Mb
Release : 2017-08-23
Category : Mathematics
ISBN : 9783319578057

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Recent Developments in Fractals and Related Fields by Julien Barral,Stéphane Seuret Pdf

This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.

Author : Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma
Publisher : American Mathematical Society
Page : 270 pages
File Size : 42,9 Mb
Release : 2024-04-18
Category : Mathematics
ISBN : 9781470472160

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Recent Developments in Fractal Geometry and Dynamical Systems by Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma Pdf

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.

Author : Julien Barral,St Phane Seuret
Publisher : Unknown
Page : 444 pages
File Size : 53,5 Mb
Release : 2010-08-01
Category : Electronic
ISBN : 0817648895

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Recent Developments in Fractals and Related Fields by Julien Barral,St Phane Seuret Pdf

Author : Ya. B. Pesin,Vaughn Climenhaga
Publisher : American Mathematical Soc.
Page : 334 pages
File Size : 45,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821848890

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Lectures on Fractal Geometry and Dynamical Systems by Ya. B. Pesin,Vaughn Climenhaga Pdf

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. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular 'chaotic' motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory - Cantor sets, Hausdorff dimension, box dimension - using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples of dynamical systems are considered and various phenomena of chaotic behaviour are discussed, including bifurcations, hyperbolicity, attractors, horseshoes, and intermittent and persistent chaos. These phenomena are naturally revealed in the course of our study of two real models from science - the FitzHugh - Nagumo model and the Lorenz system of differential equations. This book is accessible to undergraduate students and requires only standard knowledge in calculus, linear algebra, and differential equations. Elements of point set topology and measure theory are introduced as needed. This book is a result of the MASS course in analysis at Penn State University in the fall semester of 2008.

Author : Julien Barral,Stéphane Seuret
Publisher : Birkhäuser
Page : 419 pages
File Size : 55,9 Mb
Release : 2010-08-12
Category : Mathematics
ISBN : 0817648879

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Recent Developments in Fractals and Related Fields by Julien Barral,Stéphane Seuret Pdf

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?c communities with s- ni?cant developments in harmonic analysis, ranging from abstract harmonic analysis to basic applications. The title of the series re?ects the importance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the int- leaving of theory and applications and their creative symbiotic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has ?o- ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilizationwith diverse areas. The intricate and f- damental relationship between harmonic analysis and ?elds such as signal processing, partial di?erential equations (PDEs), and image processing is - ?ected in our state-of-the-art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time-frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

Author : Julien Barral,Stéphane Seuret
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 48,5 Mb
Release : 2013-02-20
Category : Mathematics
ISBN : 9780817684006

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Further Developments in Fractals and Related Fields by Julien Barral,Stéphane Seuret Pdf

This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.

Author : Michel Laurent Lapidus,Machiel Van Frankenhuysen
Publisher : American Mathematical Soc.
Page : 534 pages
File Size : 49,5 Mb
Release : 2004
Category : Ergodic theory
ISBN : 9780821836378

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Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot by Michel Laurent Lapidus,Machiel Van Frankenhuysen Pdf

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.

Author : Julien Barral,Stéphane Seuret
Publisher : Birkhäuser
Page : 288 pages
File Size : 51,5 Mb
Release : 2013-02-20
Category : Mathematics
ISBN : 0817684018

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Further Developments in Fractals and Related Fields by Julien Barral,Stéphane Seuret Pdf

This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.

Author : David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 54,7 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9780821891476

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Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics by David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen Pdf

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 Benoit 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 some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.

Author : David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen
Publisher : Unknown
Page : 410 pages
File Size : 55,6 Mb
Release : 2013
Category : Electronic books
ISBN : 1470410826

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Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I by David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen Pdf

Author : Heinz-Otto Peitgen,Peter H. Richter
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 45,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642617171

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The Beauty of Fractals by Heinz-Otto Peitgen,Peter H. Richter Pdf

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.

Author : Santo Banerjee,A. Gowrisankar,D. Easwaramoorthy,S. Nandhini,A. Manimaran
Publisher : Springer
Page : 0 pages
File Size : 54,7 Mb
Release : 2024-07-01
Category : Science
ISBN : 3031586409

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Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns by Santo Banerjee,A. Gowrisankar,D. Easwaramoorthy,S. Nandhini,A. Manimaran Pdf

This book presents selected, peer-reviewed contributions from the International Symposium on Mathematical Analysis of Fractals and Dynamical Systems - 2023 (ISMAFDS - 2023), held at the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Tamil Nadu in India during August 24-25, 2023. It offers readers an array of captivating connections between fractal theory and nonlinear dynamics across various physics sub-domains and mathematical modeling. Fractal geometry has been developed to describe irregular natural objects that defy characterization using Euclidean geometry. Fractal techniques, such as fractal dimension and fractal functions, prove effective in mathematically modeling real-world phenomena and forecasting future consequences. The impact of fractal theory on physical sciences is widely recognized, as natural phenomena frequently exhibit fractal structures. These new concepts revolutionize our understanding of the large-scale properties of matter distribution in the universe. The book aims to familiarize readers with recent developments in common fractal patterns found in statistical physics, quantum physics, and plasma physics. Furthermore, it highlights the relationship between fractals and nonlinear dynamics through innovative approaches in mathematical modeling. This publication caters to professionals in mathematics, physics, and computer science, and also serves as a helpful resource for non-specialists seeking to comprehend fractal and nonlinear dynamics concepts. It offers valuable applications for researchers in both pure and applied backgrounds of physics and engineering.

Author : David Carfi,Michel L. Lapidus,Erin P. J. Pearse,Machiel van Frankenhuijsen
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 43,7 Mb
Release : 2013-10-24
Category : Mathematics
ISBN : 9780821891483

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Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II by David Carfi,Michel L. Lapidus,Erin P. J. Pearse,Machiel van Frankenhuijsen Pdf

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.

Author : Christoph Bandt,Siegfried Graf,Martina Zähle
Publisher : Birkhäuser
Page : 286 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883801

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Fractal Geometry and Stochastics II by Christoph Bandt,Siegfried Graf,Martina Zähle Pdf

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.

Author : Peter Grabner,Wolfgang Woess
Publisher : Birkhäuser
Page : 288 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880145

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Fractals in Graz 2001 by Peter Grabner,Wolfgang Woess Pdf

This book contains the proceedings of the conference "Fractals in Graz 2001 - Analysis, Dynamics, Geometry, Stochastics" that was held in the second week of June 2001 at Graz University of Technology, in the capital of Styria, southeastern province of Austria. The scientific committee of the meeting consisted of M. Barlow (Vancouver), R. Strichartz (Ithaca), P. Grabner and W. Woess (both Graz), the latter two being the local organizers and editors of this volume. We made an effort to unite in the conference as well as in the present pro ceedings a multitude of different directions of active current work, and to bring together researchers from various countries as well as research fields that all are linked in some way with the modern theory of fractal structures. Although (or because) in Graz there is only a very small group working on fractal structures, consisting of "non-insiders", we hope to have been successful with this program of wide horizons. All papers were written upon explicit invitation by the editors, and we are happy to be able to present this representative panorama of recent work on poten tial theory, random walks, spectral theory, fractal groups, dynamic systems, fractal geometry, and more. The papers presented here underwent a refereeing process.