Hyperspaces And Fractals
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Author | : Keith R. Wicks |
Publisher | : Springer |
Total Pages | : 175 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 354046610X |
Download Fractals and Hyperspaces Book in PDF, Epub and Kindle
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 | : Gerald A. Edgar |
Publisher | : CRC Press |
Total Pages | : 384 |
Release | : 2019-03-08 |
Genre | : Science |
ISBN | : 042969122X |
Download Classics On Fractals Book in PDF, Epub and Kindle
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 | : Hans Triebel |
Publisher | : Springer Science & Business Media |
Total Pages | : 279 |
Release | : 2010-10-17 |
Genre | : Mathematics |
ISBN | : 3034800347 |
Download Fractals and Spectra Book in PDF, Epub and Kindle
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 | : Oliver Linton |
Publisher | : eBook Partnership |
Total Pages | : 64 |
Release | : 2021-05-20 |
Genre | : Mathematics |
ISBN | : 191270613X |
Download Fractals Book in PDF, Epub and Kindle
What are fractals? Why are they such fun? How do you make one? Why is a dripping tap not as random as it seems? What is chaos? Is the Mandelbrot Set really the most complex object in mathematics? In this beautifully illustrated book, fractal-hunter Oliver Linton takes us on a fascinating journey into the mathematics of fractals and chaos, diving into many kinds of self- similar structures to reveal some of the most recently discovered and intriguing patterns in science and nature. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.
Author | : Christophe Segers |
Publisher | : |
Total Pages | : |
Release | : 2016 |
Genre | : |
ISBN | : |
Download Hyperspaces and Fractals Book in PDF, Epub and Kindle
Author | : M. Fleischmann |
Publisher | : Princeton University Press |
Total Pages | : 207 |
Release | : 2014-07-14 |
Genre | : Mathematics |
ISBN | : 1400861047 |
Download Fractals in the Natural Sciences Book in PDF, Epub and Kindle
In the words of B. B. Mandelbrot's contribution to this important collection of original papers, fractal geometry is a "new geometric language, which is geared towards the study of diverse aspects of diverse objects, either mathematical or natural, that are not smooth, but rough and fragmented to the same degree at all scales." This book will be of interest to all physical and biological scientists studying these phenomena. It is based on a Royal Society discussion meeting held in 1988. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author | : Jun Kigami |
Publisher | : Cambridge University Press |
Total Pages | : 238 |
Release | : 2001-06-07 |
Genre | : Mathematics |
ISBN | : 0521793211 |
Download Analysis on Fractals Book in PDF, Epub and Kindle
This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.
Author | : Hideki Takayasu |
Publisher | : Manchester University Press |
Total Pages | : 196 |
Release | : 1990 |
Genre | : Fractals |
ISBN | : 9780719034343 |
Download Fractals in the Physical Sciences Book in PDF, Epub and Kindle
Author | : Santo Banerjee |
Publisher | : CRC Press |
Total Pages | : 142 |
Release | : 2020-03-27 |
Genre | : Mathematics |
ISBN | : 1351647628 |
Download Fractal Patterns in Nonlinear Dynamics and Applications Book in PDF, Epub and Kindle
Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the first time, fractals emphasizing mostly on stochastic fractal, and multifractals which evolves with time instead of scale-free self-similarity, are discussed. Moreover, it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.
Author | : Denny Gulick |
Publisher | : MAA |
Total Pages | : 107 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0883859718 |
Download The Beauty of Fractals Book in PDF, Epub and Kindle
The Beauty of Fractals includes six essays related to fractals, with perspectives different enough to give you a taste of the breadth of the subject. Each essay is self-contained and expository. Moreover, each of the essays is intended to be accessible to a broad audience that includes college teachers, high school teachers, advanced undergraduate students, and others who wish to learn or teach about topics in fractals that are not regularly in textbooks on fractals.