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IOP Publishing Ltd, 1997. — 306 p.The aim of this textbook is to provide the reader with an elementary introduction to fractal geometry and chaotic dynamics. These are subjects which have attracted immense interest throughout the whole range of numerate disciplines, including science, engineering, medicine, economics, and social science, to name but a few. The book may be used in part or as a whole to form an introductory course in either or both of the subject areas. The text is very much 'figure driven' as I believe that illustrations are extremely effective in conveying the concepts required for comprehension of the subject matter of the book. In addition, undue mathematical rigour is often avoided within the text in order to provide a concise treatment of specific concepts and speed the reader through the subject areas. To allow the reader a steady progression through the book, without too much jumping about from chapter to chapter, I have attempted to order the topics within the text in as logical a sequence as possible.Chapter1 provides a brief overview of both subject areas. The rest of the book is split into two parts: the first (chapters 2–4) deals with fractal geometry and its applications, while the second (chapters 5–7) tackles chaotic dynamics. Many of the methods of fractal geometry developed in the first half of the book will be used in the characterization (and comprehension) of the chaotic dynamical systems encountered in the second half of the book. Chapter2 covers regular fractals while chapter 3 covers random fractals. Chapter4 goes off at a slight tangent to investigate the fractal properties, and usefulness, of fractional Brownian motions (fBms). Initially conceived as one or two sections within chapter 3's coverage of random fractals, it soon became obvious that such an important topic deserved its own chapter. I believe that fBms have a lot to offer the scientific community, not least in the modelling of non-Fickian diffusion and natural surface roughnesses. The absence of fBms, in any detail useful to the scientist or engineer, is conspicuous in many texts. However, the reader wanting to move quickly through the text from fractals to chaos may skip chapter 4 Chapter5 deals with chaos in discrete dynamical systems. Chapter 6 covers chaos in continuous dynamical systems, and the tools necessary for the characterization of chaos are detailed in chapter 7 Among other things, chapter 7 links the fractal geometry of chapters2 and 3 with the chaotic ynamics dealt with in chapters5 and 6 In appendix A, a computer code for demonstrating chaos in the Lorenz equations is provided for use in the questions at the end of chapters 6 and 7 Appendix B illustrates the application of some of the techniques learned in chapters 6 and 7 to real experimental systems in which chaos has been observed. Seven systems are detailed briefly in this appendix and these are selected from a broad range of scientific and engineering areas.
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Cambridge University Press, 2006. — 464 p.
The chaos game.
Attractors of iterated function systems.
Another chaos game.
Codes, metrics and topologies.
Points and spaces.
Functions, mappings and transformations.
Addresses and code spaces.
Metrics on code space.
Cauchy sequences, limits and continuity.
Morgan Kaufmann, 2000. - 534 pages.
This volume is the second edition of the highly successful Fractals Everywhere. The Focus of this text is how fractal geometry can be used to model real objects in the physical world.
This edition of Fractals Everywhere is the most up-to-date fractal textbook available today.
Fractals Everywhere may be supplemented by Michael F....
The Triadic Cantor Dust.
The Sierpi´nski Gasket.
A Space of Strings.
Sets Defined Recursively.
Separable and Compact Spaces.
The Hausdorff Metric.
Metrics for Strings.
Oxford University Press, 2012. - 431 p. - This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated...
Second Edition. — VCH, 1994. — 453 Pages. — ISBN: 3527290788.
Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the descriptive power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. The second edition of this...
2-е изд., испр. — М.: Физматлит, 2003. — 296 с. Обобщаются известные и предлагаются новые методы математического моделирования нелинейных динамических систем. На простых примерах пояснены механизмы возникновения динамического хаоса, самоорганизации и др. Предложен принципиально новый подход к моделированию динамических систем, основанный на теории возможностей и нечеткой...