Fractals And Hyperspaces

Author : Keith R. Wicks
Publisher : Springer
ISBN 13 : 354046610X
Total Pages : 175 pages
Book Rating : 4.09/5 ( download)

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Download or read book Fractals and Hyperspaces written by Keith R. Wicks and published by Springer. This book was released on 2006-11-14 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal", i.e. have infinite detail in a certain sense. These ideas have considerable scope for further development, and a list of problems and lines of research is included.

Author : Marius Mitrea
Publisher : Springer
ISBN 13 : 9783540578840
Total Pages : 136 pages
Book Rating : 4.46/5 ( download)

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Download or read book Clifford Wavelets, Singular Integrals, and Hardy Spaces written by Marius Mitrea and published by Springer. This book was released on 1994-04-28 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the extensions of basic Fourier Analysis techniques to the Clifford algebra framework. Topics covered: construction of Clifford-valued wavelets, Calderon-Zygmund theory for Clifford valued singular integral operators on Lipschitz hyper-surfaces, Hardy spaces of Clifford monogenic functions on Lipschitz domains. Results are applied to potential theory and elliptic boundary value problems on non-smooth domains. The book is self-contained to a large extent and well-suited for graduate students and researchers in the areas of wavelet theory, Harmonic and Clifford Analysis. It will also interest the specialists concerned with the applications of the Clifford algebra machinery to Mathematical Physics.

Author : Christophe Segers
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.77/5 ( download)

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Download or read book Hyperspaces and Fractals written by Christophe Segers and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Hans Triebel
Publisher : Springer Science & Business Media
ISBN 13 : 3034800339
Total Pages : 278 pages
Book Rating : 4.34/5 ( download)

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Download or read book Fractals and Spectra written by Hans Triebel and published by Springer Science & Business Media. This book was released on 2010-10-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Most of the presented material is published here for the first time.

Author : Gerald A. Edgar
Publisher : CRC Press
ISBN 13 : 042969122X
Total Pages : 384 pages
Book Rating : 4.25/5 ( download)

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Download or read book Classics On Fractals written by Gerald A. Edgar and published by CRC Press. This book was released on 2019-03-08 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Read the masters! Experience has shown that this is good advice for the serious mathematics student. This book contains a selection of the classical mathematical papers related to fractal geometry. For the convenience of the student or scholar wishing to learn about fractal geometry, nineteen of these papers are collected here in one place. Twelve of the nineteen have been translated into English from German, French, or Russian. In many branches of science, the work of previous generations is of interest only for historical reasons. This is much less so in mathematics.1 Modern-day mathematicians can learn (and even find good ideas) by reading the best of the papers of bygone years. In preparing this volume, I was surprised by many of the ideas that come up.

Author : Stephen Lipscomb
Publisher : Springer Science & Business Media
ISBN 13 : 0387854940
Total Pages : 259 pages
Book Rating : 4.46/5 ( download)

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Download or read book Fractals and Universal Spaces in Dimension Theory written by Stephen Lipscomb and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessarily separable metric). The classical theory is now well documented in several books. This monograph is the first book to unify the modern theory from 1960-2007. Like the classical theory, the modern theory fundamentally involves the unit interval. Unique features include: * The use of graphics to illustrate the fractal view of these spaces; * Lucid coverage of a range of topics including point-set topology and mapping theory, fractal geometry, and algebraic topology; * A final chapter contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings; * Each chapter contains a comment section that provides historical context with references that serve as a bridge to the literature. This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. Being the first monograph to focus on the connection between generalized fractals and universal spaces in dimension theory, it will be a natural text for graduate seminars or self-study - the interested reader will find many relevant open problems which will create further research into these topics.

Author : Stephen Lipscomb
Publisher : Springer
ISBN 13 : 9780387854939
Total Pages : 242 pages
Book Rating : 4.32/5 ( download)

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Download or read book Fractals and Universal Spaces in Dimension Theory written by Stephen Lipscomb and published by Springer. This book was released on 2008-12-03 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessarily separable metric). The classical theory is now well documented in several books. This monograph is the first book to unify the modern theory from 1960-2007. Like the classical theory, the modern theory fundamentally involves the unit interval. Unique features include: * The use of graphics to illustrate the fractal view of these spaces; * Lucid coverage of a range of topics including point-set topology and mapping theory, fractal geometry, and algebraic topology; * A final chapter contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings; * Each chapter contains a comment section that provides historical context with references that serve as a bridge to the literature. This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. Being the first monograph to focus on the connection between generalized fractals and universal spaces in dimension theory, it will be a natural text for graduate seminars or self-study - the interested reader will find many relevant open problems which will create further research into these topics.

Author : Andrzej Katunin
Publisher : CRC Press
ISBN 13 : 135180121X
Total Pages : 91 pages
Book Rating : 4.18/5 ( download)

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Download or read book A Concise Introduction to Hypercomplex Fractals written by Andrzej Katunin and published by CRC Press. This book was released on 2017-10-05 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents concisely the full story on complex and hypercomplex fractals, starting from the very first steps in complex dynamics and resulting complex fractal sets, through the generalizations of Julia and Mandelbrot sets on a complex plane and the Holy Grail of the fractal geometry – a 3D Mandelbrot set, and ending with hypercomplex, multicomplex and multihypercomplex fractal sets which are still under consideration of scientists. I tried to write this book in a possibly simple way in order to make it understandable to most people whose math knowledge covers the fundamentals of complex numbers only. Moreover, the book is full of illustrations of generated fractals and stories concerned with great mathematicians, number spaces and related fractals. In the most cases only information required for proper understanding of a nature of a given vector space or a construction of a given fractal set is provided, nevertheless a more advanced reader may treat this book as a fundamental compendium on hypercomplex fractals with references to purely scientific issues like dynamics and stability of hypercomplex systems.

Author : Stephen Semmes
Publisher : Oxford University Press
ISBN 13 : 9780198508069
Total Pages : 180 pages
Book Rating : 4.69/5 ( download)

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Download or read book Some Novel Types of Fractal Geometry written by Stephen Semmes and published by Oxford University Press. This book was released on 2001 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with fractal geometries that have features similar to ones of ordinary Euclidean spaces, while at the same time being quite different from Euclidean spaces.. A basic example of this feature considered is the presence of Sobolev or Poincaré inequalities, concerning the relationship between the average behavior of a function and the average behavior of its small-scale oscillations. Remarkable results in the last few years through Bourdon-Pajot and Laakso have shown that there is much more in the way of geometries like this than have been realized, only examples related to nilpotent Lie groups and Carnot metrics were known previously. On the other had, 'typical' fractals that might be seen in pictures do not have these same kinds of features. This text examines these topics in detail and will interest graduate students as well as researchers in mathematics and various aspects of geometry and analysis.

Author : Paul S. Addison
Publisher : CRC Press
ISBN 13 : 9780849384431
Total Pages : 276 pages
Book Rating : 4.35/5 ( download)

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Download or read book Fractals and Chaos written by Paul S. Addison and published by CRC Press. This book was released on 1997-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study.