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Encounters With Chaos
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Book Synopsis Encounters with Chaos and Fractals, Second Edition by : Denny Gulick
Download or read book Encounters with Chaos and Fractals, Second Edition written by Denny Gulick and published by CRC Press. This book was released on 2012-04-26 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now with an extensive introduction to fractal geometry Revised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. Laying the groundwork for later chapters, the text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the author goes on to introduce famous infinitely complicated fractals. He analyzes them and explains how to obtain computer renditions of them. The book concludes with the famous Julia sets and the Mandelbrot set. With more than enough material for a one-semester course, this book gives readers an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry. It shows how these subjects continue to grow within mathematics and in many other disciplines.
Book Synopsis Encounters with Chaos by : Denny Gulick
Download or read book Encounters with Chaos written by Denny Gulick and published by McGraw-Hill Science, Engineering & Mathematics. This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Celestial Encounters by : Florin Diacu
Download or read book Celestial Encounters written by Florin Diacu and published by Princeton University Press. This book was released on 2020-12-08 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos. Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics. In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincaré. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.
Book Synopsis Encounter with Chaos by : Joachim Peinke
Download or read book Encounter with Chaos written by Joachim Peinke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our life is a highly nonlinear process. It starts with birth and ends with death; in between there are a lot of ups and downs. Quite often, we believe that stable and steady situations, probably easy to capture by linearization, are paradisiacal, but already after a short period of everyday routine we usually become bored and seek change, that is, nonlinearities. If we reflect for a while, we notice that our life and our perceptions are mainly determined by nonlinear phenomena, for example, events occurring suddenly and unexpectedly. One may be surprised by how long scientists tried to explain our world by models based on a linear ansatz. Due to the lack of typical nonlinear patterns, although everybody experienced nonlinearities, nobody could classify them and, thus,· study them further. The discoveries of the last few decades have finally provided access to the world of nonlinear phenomena and have initiated a unique inter disciplinary field of research: nonlinear science. In contrast to the general tendency of science to become more branched out and specialized as the result of any progress, nonlinear science has brought together many different disciplines. This has been motivated not only by the immense importance of nonlinearities for science, but also by the wonderful simplicity ohhe concepts. Models like the logistic map can be easily understood by high school students and have brought revolutionary new insights into our scientific under standing.
Book Synopsis Encounters with Chaos by : Denny Gulick
Download or read book Encounters with Chaos written by Denny Gulick and published by . This book was released on 1992 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Essence Of Chaos by : Flavio Lorenzelli
Download or read book The Essence Of Chaos written by Flavio Lorenzelli and published by CRC Press. This book was released on 2003-09-02 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field. Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals. As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time.
Book Synopsis Chaos in the Contact Zone by : Stephanie Wodianka
Download or read book Chaos in the Contact Zone written by Stephanie Wodianka and published by transcript Verlag. This book was released on 2017-06-30 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cultural encounters are often being stylized not only as experiences of uncontrollability and unpredictability par excellence, but also as challenges to planning and predicting. The history, the different forms and the consequences of this phenomenon are the main issues discussed in this volume. The contributions show that chaos and control are not mutually exclusive in the "contact zone" (Mary Louise Pratt); on the contrary, they stand in relation to each other - be it as a competence or as an interpretive scheme.
Book Synopsis Encounters with Chaos and Fractals by : Denny Gulick
Download or read book Encounters with Chaos and Fractals written by Denny Gulick and published by CRC Press. This book was released on 2012-04-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now with an extensive introduction to fractal geometryRevised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. It incorporates important mathematical concepts associated with these areas and backs up the definitions an
Book Synopsis Everyday Chaos by : David Weinberger
Download or read book Everyday Chaos written by David Weinberger and published by Harvard Business Press. This book was released on 2019-04-23 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Make. More. Future. Artificial intelligence, big data, modern science, and the internet are all revealing a fundamental truth: The world is vastly more complex and unpredictable than we've allowed ourselves to see. Now that technology is enabling us to take advantage of all the chaos it's revealing, our understanding of how things happen is changing--and with it our deepest strategies for predicting, preparing for, and managing our world. This affects everything, from how we approach our everyday lives to how we make moral decisions and how we run our businesses. Take machine learning, which makes better predictions about weather, medical diagnoses, and product performance than we do--but often does so at the expense of our understanding of how it arrived at those predictions. While this can be dangerous, accepting it is also liberating, for it enables us to harness the complexity of an immense amount of data around us. We are also turning to strategies that avoid anticipating the future altogether, such as A/B testing, Minimum Viable Products, open platforms, and user-modifiable video games. We even take for granted that a simple hashtag can organize unplanned, leaderless movements such as #MeToo. Through stories from history, business, and technology, philosopher and technologist David Weinberger finds the unifying truths lying below the surface of the tools we take for granted--and a future in which our best strategy often requires holding back from anticipating and instead creating as many possibilities as we can. The book’s imperative for business and beyond is simple: Make. More. Future. The result is a world no longer focused on limitations but optimized for possibilities.
Book Synopsis Encounters with Chaos and Fractals, Third Edition by : Denny Gulick
Download or read book Encounters with Chaos and Fractals, Third Edition written by Denny Gulick and published by CRC Press. This book was released on 2018-08 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This popular text provides an accessible introduction to chaotic dynamics and fractal geometry. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. With more than enough material for a one-semester course, this book gives readers an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry. It shows how these subjects continue to grow within mathematics and in many other disciplines. A set of concept-oriented problems for each chapter, and new examples and exercises are included in this edition.
Book Synopsis The Topology of Chaos by : Robert Gilmore
Download or read book The Topology of Chaos written by Robert Gilmore and published by John Wiley & Sons. This book was released on 2012-09-19 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep understanding of the structure of strange attractors, how they are classified, and how the information required to identify and classify a strange attractor can be extracted from experimental data. In its first edition, the Topology of Chaos has been a valuable resource for physicist and mathematicians interested in the topological analysis of dynamical systems. Since its publication in 2002, important theoretical and experimental advances have put the topological analysis program on a firmer basis. This second edition includes relevant results and connects the material to other recent developments. Following significant improvements will be included: * A gentler introduction to the topological analysis of chaotic systems for the non expert which introduces the problems and questions that one commonly encounters when observing a chaotic dynamics and which are well addressed by a topological approach: existence of unstable periodic orbits, bifurcation sequences, multistability etc. * A new chapter is devoted to bounding tori which are essential for achieving generality as well as for understanding the influence of boundary conditions. * The new edition also reflects the progress which had been made towards extending topological analysis to higher-dimensional systems by proposing a new formalism where evolving triangulations replace braids. * There has also been much progress in the understanding of what is a good representation of a chaotic system, and therefore a new chapter is devoted to embeddings. * The chapter on topological analysis program will be expanded to cover traditional measures of chaos. This will help to connect those readers who are familiar with those measures and tests to the more sophisticated methodologies discussed in detail in this book. * The addition of the Appendix with both frequently asked and open questions with answers gathers the most essential points readers should keep in mind and guides to corresponding sections in the book. This will be of great help to those who want to selectively dive into the book and its treatments rather than reading it cover to cover. What makes this book special is its attempt to classify real physical systems (e.g. lasers) using topological techniques applied to real date (e.g. time series). Hence it has become the experimenter?s guidebook to reliable and sophisticated studies of experimental data for comparison with candidate relevant theoretical models, inevitable to physicists, mathematicians, and engineers studying low-dimensional chaotic systems.
Book Synopsis Chaos and Fractals by : Heinz-Otto Peitgen
Download or read book Chaos and Fractals written by Heinz-Otto Peitgen and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 1013 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.
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 Nonlinear Dynamics and Chaos by : Steven H. Strogatz
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Book Synopsis Chaos and Night by : Henry de Montherlant
Download or read book Chaos and Night written by Henry de Montherlant and published by New York Review of Books. This book was released on 2009-02-17 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Don Celestino is old and bitter and afraid, an impossible man. An anarchist who has been in exile from his native Spain for more than twenty years, he lives with his daughter in Paris, but in his mind he is still fighting the Spanish Civil War. He fulminates against the daily papers; he brags about his past exploits. He has become bigoted, self-important, and obsessed; a bully to his fellow exiles and a tyrant to his daughter, Pascualita. Then a family member dies in Madrid and there is an inheritance to sort out. Pascualita wants to go to Spain, which is supposedly opening up in response to the 1960s, and Don Celestino feels he has no choice but to follow. He is full of dread and desire, foreseeing a heroic last confrontation with his enemies, but what he encounters instead is a new commercialized Spain that has no time for the past, much less for him. Or so it seems. Because the last act of Don Celestino’s dizzying personal drama will prove that though “there is nothing serious . . . , there is tragedy.” An astonishing modern take on Don Quixote, Chaos and Night untangles the ties between politics and paranoia, self-loathing and self-pity, rage and remorse. It is the darkly funny final flowering of the art of Henry de Montherlant, a solitary and scarifying modern master whose work, admired by Graham Greene and Albert Camus, is sure to appeal to contemporary readers of Thomas Bernhard and Roberto Bolaño.
Book Synopsis Discrete Encounters by : Craig Bauer
Download or read book Discrete Encounters written by Craig Bauer and published by CRC Press. This book was released on 2020-05-14 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open problems. This book focuses on the historical development of the subject and provides fascinating details of the people behind the mathematics, along with their motivations, deepening readers’ appreciation of mathematics. This unique book covers many of the same topics found in traditional textbooks, but does so in an alternative, entertaining style that better captures readers’ attention. In addition to standard discrete mathematics material, the author shows the interplay between the discrete and the continuous and includes high-interest topics such as fractals, chaos theory, cellular automata, money-saving financial mathematics, and much more. Not only will readers gain a greater understanding of mathematics and its culture, they will also be encouraged to further explore the subject. Long lists of references at the end of each chapter make this easy. Highlights: Features fascinating historical context to motivate readers Text includes numerous pop culture references throughout to provide a more engaging reading experience Its unique topic structure presents a fresh approach The text’s narrative style is that of a popular book, not a dry textbook Includes the work of many living mathematicians Its multidisciplinary approach makes it ideal for liberal arts mathematics classes, leisure reading, or as a reference for professors looking to supplement traditional courses Contains many open problems Profusely illustrated
Book Synopsis Chaos and Dynamical Systems by : David P. Feldman
Download or read book Chaos and Dynamical Systems written by David P. Feldman and published by Princeton University Press. This book was released on 2019-08-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
