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The Universal Mandelbrot Set
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Book Synopsis The Universal Mandelbrot Set by : V. Dolotin
Download or read book The Universal Mandelbrot Set written by V. Dolotin and published by World Scientific. This book was released on 2006 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the structure of the Mandelbrot set OCo a remarkable and important feature of modern theoretical physics, related to chaos and fractals and simultaneously to analytical functions, Riemann surfaces, phase transitions and string theory. The Mandelbrot set is one of the bridges connecting the world of chaos and order. The authors restrict consideration to discrete dynamics of a single variable . This restriction preserves the most essential properties of the subject, but drastically simplifies computer simulations and the mathematical formalism. The coverage includes a basic description of the structure of the set of orbits and pre-orbits associated with any map of an analytic space into itself. A detailed study of the space of orbits (the algebraic Julia set) as a whole, together with related attributes, is provided. Also covered are: moduli space in the space of maps and the classification problem for analytic maps, the relation of the moduli space to the bifurcations (topology changes) of the set of orbits, a combinatorial description of the moduli space (Mandelbrot and secondary Mandelbrot sets) and the corresponding invariants (discriminants and resultants), and the construction of the universal discriminant of analytic functions in terms of series coefficients. The book concludes by solving the case of the quadratic map using the theory and methods discussed earlier. Sample Chapter(s). Chapter 1: Introduction (219 KB). Contents: Notions and Notation; Summary; Fragments of Theory; Map f(x) = X 2 + c: From Standard Example to General Conclusions. Readership: Researchers and students in algebra & number theory and mathematical physics."
Book Synopsis Universal Mandelbrot Set, The: Beginning Of The Story by : Alexei Morozov
Download or read book Universal Mandelbrot Set, The: Beginning Of The Story written by Alexei Morozov and published by World Scientific. This book was released on 2006-10-09 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the structure of the Mandelbrot set — a remarkable and important feature of modern theoretical physics, related to chaos and fractals and simultaneously to analytical functions, Riemann surfaces, phase transitions and string theory. The Mandelbrot set is one of the bridges connecting the world of chaos and order.The authors restrict consideration to discrete dynamics of a single variable. This restriction preserves the most essential properties of the subject, but drastically simplifies computer simulations and the mathematical formalism.The coverage includes a basic description of the structure of the set of orbits and pre-orbits associated with any map of an analytic space into itself. A detailed study of the space of orbits (the algebraic Julia set) as a whole, together with related attributes, is provided. Also covered are: moduli space in the space of maps and the classification problem for analytic maps, the relation of the moduli space to the bifurcations (topology changes) of the set of orbits, a combinatorial description of the moduli space (Mandelbrot and secondary Mandelbrot sets) and the corresponding invariants (discriminants and resultants), and the construction of the universal discriminant of analytic functions in terms of series coefficients. The book concludes by solving the case of the quadratic map using the theory and methods discussed earlier.
Book Synopsis The Mandelbrot Set, Theme and Variations by : Lei Tan
Download or read book The Mandelbrot Set, Theme and Variations written by Lei Tan and published by Cambridge University Press. This book was released on 2000-04-13 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematic exposition of current knowledge about the Mandelbrot set, discussing the latest research and results.
Book Synopsis Fractals and Chaos by : Benoit Mandelbrot
Download or read book Fractals and Chaos written by Benoit Mandelbrot and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer. The text includes some items not previously published.
Book Synopsis In Search of the Riemann Zeros by : Michel Laurent Lapidus
Download or read book In Search of the Riemann Zeros written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2008 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possible--or, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line.
Book Synopsis Introduction to Non-linear Algebra by : Valeri? Valer?evich Dolotin
Download or read book Introduction to Non-linear Algebra written by Valeri? Valer?evich Dolotin and published by World Scientific. This book was released on 2007 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Literaturverz. S. 267 - 269
Book Synopsis Introduction To Non-linear Algebra by : Morozov Alexei
Download or read book Introduction To Non-linear Algebra written by Morozov Alexei and published by World Scientific Publishing Company. This book was released on 2007-10-02 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text presents the new domain of consistent non-linear counterparts for all basic objects and tools of linear algebra, and develops an adequate calculus for solving non-linear algebraic and differential equations. It reveals the non-linear algebraic activity as an essentially wider and diverse field with its own original methods, of which the linear one is a special restricted case.This volume contains a detailed and comprehensive description of basic objects and fundamental techniques arising from the theory of non-linear equations, which constitute the scope of what should be called non-linear algebra. The objects of non-linear algebra are presented in parallel with the corresponding linear ones, followed by an exposition of specific non-linear properties treated with the use of classical (such as the Koszul complex) and original new tools. This volume extensively uses a new diagram technique and is enriched with a variety of illustrations throughout the text. Thus, most of the material is new and is clearly exposed, starting from the elementary level. With the scope of its perspective applications spreading from general algebra to mathematical physics, it will interest a broad audience of physicists; mathematicians, as well as advanced undergraduate and graduate students.
Book Synopsis Quantum Phaith by : Jeffrey Strickland
Download or read book Quantum Phaith written by Jeffrey Strickland and published by Lulu.com. This book was released on 2011-09-13 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Typically, scientist try to either prove or disprove Scripture, as it relates the Creation story, then write books about their findings. Quantum Phaith is not one of those books. Instead, the author accepts the Word of God, a priori. Quantum Phaith is a journey through elementary quantum mechanics, chaos theory, number theory, and more. This is also a journey through the author's faith and what he has discovered about science through it; his faith has been unshaken by science and mathematics. Quantum Phaith examines the Creation account, using the results to support what scientists have discovered about the universe. Their discoveries were already contained in the Bible! Quantum Phaith portrays God as perfect, His creation perfect in every regard. Imperfection was introduced by the Fall or Man. God is all-powerful, all-knowing, transcends time, space, and our understanding. God is order, and you will find that chaos contains unobservable order! Quantum Phaith will make you think. It may change your life.
Book Synopsis Fractals, Chaos, Power Laws by : Manfred Schroeder
Download or read book Fractals, Chaos, Power Laws written by Manfred Schroeder and published by Courier Corporation. This book was released on 2009-08-21 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.
Book Synopsis The Fractal Geometry of Nature by : Benoit Mandelbrot
Download or read book The Fractal Geometry of Nature written by Benoit Mandelbrot and published by Echo Point Books & Media, LLC. This book was released on 2021-07-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.
Book Synopsis A First Course in Computational Fluid Dynamics by : H. Aref
Download or read book A First Course in Computational Fluid Dynamics written by H. Aref and published by Cambridge University Press. This book was released on 2017-10-12 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid mechanics is a branch of classical physics that has a rich tradition in applied mathematics and numerical methods. It is at work virtually everywhere, from nature to technology. This broad and fundamental coverage of computational fluid dynamics (CFD) begins with a presentation of basic numerical methods and flows into a rigorous introduction to the subject. A heavy emphasis is placed on the exploration of fluid mechanical physics through CFD, making this book an ideal text for any new course that simultaneously covers intermediate fluid mechanics and computation. Ample examples, problems and computer exercises are provided to allow students to test their understanding of a variety of numerical methods for solving flow physics problems, including the point-vortex method, numerical methods for hydrodynamic stability analysis, spectral methods and traditional CFD topics.
Book Synopsis European Congress of Mathematics by : Ari Laptev
Download or read book European Congress of Mathematics written by Ari Laptev and published by European Mathematical Society. This book was released on 2005 with total page 906 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris, 1992, Budapest, 1996, and Barcelona, 2000, the Fourth European Congress of Mathematics took place in Stockholm, Sweden, June 27 to July 2, 2004, with 913 participants from 65 countries. Apart from seven plenary and thirty three invited lectures, there were six Science Lectures covering the most relevant aspects of mathematics in science and technology. Moreover, twelve projects of the EU Research Training Networks in Mathematics and Information Sciences, as well as Programmes from the European Science Foundation in Physical and Engineering Sciences, were presented. Ten EMS Prizes were awarded to young European mathematicians who have made a particular contribution to the progress of mathematics. Five of the prizewinners were independently chosen by the 4ECM Scientific Committee as plenary or invited speakers. The other five prizewinners gave their lectures in parallel sessions. Most of these contributions are now collected in this volume, providing a permanent record of so much that is best in mathematics today.
Book Synopsis Computability of Julia Sets by : Mark Braverman
Download or read book Computability of Julia Sets written by Mark Braverman and published by Springer Science & Business Media. This book was released on 2009-02-08 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathematical content. Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computer screen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. This result is striking - it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized. The book summarizes the present knowledge (most of it from the authors' own work) about the computational properties of Julia sets in a self-contained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems.
Book Synopsis Fractals in Physics by : L. Pietronero
Download or read book Fractals in Physics written by L. Pietronero and published by Elsevier. This book was released on 2012-12-02 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractals in Physics
Book Synopsis Magical Mathematics by : Persi Diaconis
Download or read book Magical Mathematics written by Persi Diaconis and published by Princeton University Press. This book was released on 2015-10-13 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Magical Mathematics reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge. For example, the Gilbreath principle--a fantastic effect where the cards remain in control despite being shuffled--is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat's last theorem. Diaconis and Graham are mathematicians as well as skilled performers with decades of professional experience between them. In this book they share a wealth of conjuring lore, including some closely guarded secrets of legendary magicians. Magical Mathematics covers the mathematics of juggling and shows how the I Ching connects to the history of probability and magic tricks both old and new. It tells the stories--and reveals the best tricks--of the eccentric and brilliant inventors of mathematical magic. Magical Mathematics exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card monte, traces the history of mathematical magic back to the thirteenth century and the oldest mathematical trick--and much more"-
Book Synopsis Explorations in Complex Analysis by : Michael A. Brilleslyper
Download or read book Explorations in Complex Analysis written by Michael A. Brilleslyper and published by American Mathematical Soc.. This book was released on 2012-12-31 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
Download or read book Deep Creativity written by Victor Shamas and published by Morgan James Publishing. This book was released on 2017-09-12 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep Creativity reveals the findings of Victor Shamas’ 30-year exploration of the creative process. Rather than observing creativity in others, he delved into the experience directly in order to uncover hidden truths and break free of common misconceptions. Deep Creativity turns fundamental assumptions about creativity on their head while offering fresh perspectives on the scientific method, fractals, Maslow’s hierarchy of needs, plate tectonics, mind and consciousness, hero myths, the life cycle, sleep and dreams, mothers’ intuition, the nature of wisdom, peak experiences, and even the Gospels. Written from a research psychologist’s perspective, Deep Creativity portrays the creative experience as a bold adventure filled with passion, turmoil, inspiration, sacrifice, sheer joy, self-transcendence, and unconditional love.
