Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii

Author : David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 45,6 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 L. Lapidus,Erin P. J. Pearse,Machiel van Frankenhuijsen
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 46,6 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 : David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen
Publisher : Unknown
Page : 410 pages
File Size : 46,9 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 : Herb Kunze,Davide La Torre,Franklin Mendivil,Edward R. Vrscay
Publisher : Springer Science & Business Media
Page : 417 pages
File Size : 47,9 Mb
Release : 2011-11-18
Category : Mathematics
ISBN : 9781461418917

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Fractal-Based Methods in Analysis by Herb Kunze,Davide La Torre,Franklin Mendivil,Edward R. Vrscay Pdf

The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters. For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises. This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences. Herb Kunze is a professor of mathematics at the University of Guelph in Ontario. Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan. Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia. Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo in Ontario. The major focus of their research is on fractals and the applications of fractals.

Author : Ya. B. Pesin,Vaughn Climenhaga
Publisher : American Mathematical Soc.
Page : 334 pages
File Size : 43,5 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 : P. Fischer
Publisher : CRC Press
Page : 282 pages
File Size : 52,5 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000154221

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Chaos, Fractals, and Dynamics by P. Fischer Pdf

This book contains eighteen papers, all more-or-less linked to the theory of dynamical systems together with related studies of chaos and fractals. It shows many fractal configurations that were generated by computer calculations of underlying two-dimensional maps.

Author : Michel Laurent Lapidus,Machiel Van Frankenhuysen
Publisher : American Mathematical Soc.
Page : 534 pages
File Size : 49,8 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 : Springer Science & Business Media
Page : 296 pages
File Size : 46,7 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 : Julien Barral,Stéphane Seuret
Publisher : Birkhäuser
Page : 312 pages
File Size : 51,8 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 : Robert L. Devaney,Kathleen T. Alligood
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 54,8 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821801376

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Chaos and Fractals: The Mathematics Behind the Computer Graphics by Robert L. Devaney,Kathleen T. Alligood Pdf

"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.

Author : Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma
Publisher : American Mathematical Society
Page : 270 pages
File Size : 47,8 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 : James W. Cogdell,Freydoon Shahidi,David Soudry
Publisher : American Mathematical Soc.
Page : 454 pages
File Size : 44,7 Mb
Release : 2014-04-01
Category : Mathematics
ISBN : 9780821893944

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Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro by James W. Cogdell,Freydoon Shahidi,David Soudry Pdf

This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.

Author : Julien Barral,Stéphane Seuret
Publisher : Birkhäuser
Page : 288 pages
File Size : 40,9 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 : Y. Takahashi
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461303213

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Algorithms, Fractals, and Dynamics by Y. Takahashi Pdf

In 1992 two successive symposia were held in Japan on algorithms, fractals and dynamical systems. The first one was Hayashibara Forum '92: International Symposium on New Bases for Engineering Science, Algorithms, Dynamics and Fractals held at Fujisaki Institute of Hayashibara Biochemical Laboratories, Inc. in Okayama during November 23-28 in which 49 mathematicians including 19 from abroad participated. They include both pure and applied mathematicians of diversified backgrounds and represented 11 coun tries. The organizing committee consisted of the following domestic members and Mike KEANE from Delft: Masayosi HATA, Shunji ITO, Yuji ITO, Teturo KAMAE (chairman), Hitoshi NAKADA, Satoshi TAKAHASHI, Yoichiro TAKAHASHI, Masaya YAMAGUTI The second one was held at the Research Institute for Mathematical Science at Kyoto University from November 30 to December 2 with emphasis on pure mathematical side in which more than 80 mathematicians participated. This volume is a partial record of the stimulating exchange of ideas and discussions which took place in these two symposia.

Author : Vyjayanthi Chari,Jacob Greenstein,Kailash C. Misra,K. N. Raghavan,Sankaran Viswanath
Publisher : American Mathematical Soc.
Page : 222 pages
File Size : 51,6 Mb
Release : 2013-11-25
Category : Mathematics
ISBN : 9780821890370

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Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory by Vyjayanthi Chari,Jacob Greenstein,Kailash C. Misra,K. N. Raghavan,Sankaran Viswanath Pdf

This volume contains the proceedings of the International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, held August 12-16, 2010, at the National Institute of Advanced Studies, Bangalore, India, and the follow-up conference held May 18-20, 2012, at the University of California, USA. It contains original research and survey articles on various topics in the theory of representations of Lie algebras, quantum groups and algebraic groups, including crystal bases, categorification, toroidal algebras and their generalisations, vertex algebras, Hecke algebras, Kazhdan-Lusztig bases, $q$-Schur algebras, and Weyl algebras.