Measure Topology And Fractal Geometry
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Measure Topology And Fractal Geometry
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Author : Gerald Edgar
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-23
Measure Topology And Fractal Geometry written by Gerald Edgar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-23 with Mathematics categories.
From reviews of the first edition: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology...the book also contains many good illustrations of fractals (including 16 color plates)." Mathematics Teaching "The book can be recommended to students who seriously want to know about the mathematical foundation of fractals, and to lecturers who want to illustrate a standard course in metric topology by interesting examples." Christoph Bandt, Mathematical Reviews "...not only intended to fit mathematics students who wish to learn fractal geometry from its beginning but also students in computer science who are interested in the subject. Especially, for the last students the author gives the required topics from metric topology and measure theory on an elementary level. The book is written in a very clear style and contains a lot of exercises which should be worked out." H.Haase, Zentralblatt About the second edition: Changes throughout the text, taking into account developments in the subject matter since 1990; Major changes in chapter 6. Since 1990 it has become clear that there are two notions of dimension that play complementary roles, so the emphasis on Hausdorff dimension will be replaced by the two: Hausdorff dimension and packing dimension. 6.1 will remain, but a new section on packing dimension will follow it, then the old sections 6.2--6.4 will be re-written to show both types of dimension; Substantial change in chapter 7: new examples along with recent developments; Sections rewritten to be made clearer and more focused.
Measure Topology And Fractal Geometry
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Author : Gerald A. Edgar
language : en
Publisher:
Release Date : 2014-01-15
Measure Topology And Fractal Geometry written by Gerald A. Edgar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Measure Topology And Fractal Geometry
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Author : Gerald Edgar
language : en
Publisher: Springer
Release Date : 2008-11-01
Measure Topology And Fractal Geometry written by Gerald Edgar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.
Measure Topology And Fractal Geometry
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Author : Gerald A. Edgar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Measure Topology And Fractal Geometry written by Gerald A. Edgar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1
Integral Probability And Fractal Measures
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Author : Gerald A. Edgar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Integral Probability And Fractal Measures written by Gerald A. Edgar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
This book may be considered a continuation of my Springer-Verlag text Mea sure, Topology, and Fractal Geometry. It presupposes some elementary knowl edge of fractal geometry and the mathematics behind fractal geometry. Such knowledge might be obtained by study of Measure, Topology, and Fractal Ge ometry or by study of one of the other mathematically oriented texts (such as [13] or [87]). I hope this book will be appropriate to mathematics students at the beginning graduate level in the U.S. Most references are numbered and may be found at the end of the book; but Measure, Topology, and Fractal Geometry is referred to as [ MTFG]. One of the reviews of [MTFG] says that it "sacrific[es] breadth of coverage 1 for systematic development" -although I did not have it so clearly formulated as that in my mind at the time I was writing the book, I think that remark is exactly on target. That sacrifice has been made in this volume as well. In many cases, I do not include the most general or most complete form of a result. Sometimes I have only an example of an important development. The goal was to omit most material that is too tedious or that requires too much background.
Assouad Dimension And Fractal Geometry
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Author : Jonathan M. Fraser
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-29
Assouad Dimension And Fractal Geometry written by Jonathan M. Fraser and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-29 with Mathematics categories.
The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.
Integral Probability And Fractal Measures
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Author : Gerald A Edgar
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-12-05
Integral Probability And Fractal Measures written by Gerald A Edgar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-05 with Mathematics categories.
Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid the discussion of fractals, and follows Edgars Measure, Topology, and Fractal Geometry. With exercises throughout, this is and ideal text for beginning graduate students both in the classroom and for self-study.
Fractal Geometry And Stochastics Ii
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Author : Christoph Bandt
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Fractal Geometry And Stochastics Ii written by Christoph Bandt and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The second conference on Fractal Geometry and Stochastics was held at Greifs wald/Koserow, Germany from August 28 to September 2, 1998. Four years had passed after the first conference with this theme and during this period the interest in the subject had rapidly increased. More than one hundred mathematicians from twenty-two countries attended the second conference and most of them presented their newest results. Since it is impossible to collect all these contributions in a book of moderate size we decided to ask the 13 main speakers to write an account of their subject of interest. The corresponding articles are gathered in this volume. Many of them combine a sketch of the historical development with a thorough discussion of the most recent results of the fields considered. We believe that these surveys are of benefit to the readers who want to be introduced to the subject as well as to the specialists. We also think that this book reflects the main directions of research in this thriving area of mathematics. We express our gratitude to the Deutsche Forschungsgemeinschaft whose financial support enabled us to organize the conference. The Editors Introduction Fractal geometry deals with geometric objects that show a high degree of irregu larity on all levels of magnitude and, therefore, cannot be investigated by methods of classical geometry but, nevertheless, are interesting models for phenomena in physics, chemistry, biology, astronomy and other sciences.
Fractal Dimension For Fractal Structures
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Author : Manuel Fernández-Martínez
language : en
Publisher: Springer
Release Date : 2019-04-23
Fractal Dimension For Fractal Structures written by Manuel Fernández-Martínez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-23 with Mathematics categories.
This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.
Fractional Dynamics
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Author : Vasily E. Tarasov
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-04
Fractional Dynamics written by Vasily E. Tarasov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-04 with Science categories.
"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.