Encounter With Chaos
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| Author | : Joachim Peinke |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 298 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642776256 |
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.
| Author | : Denny Gulick |
| Publisher | : McGraw-Hill Science, Engineering & Mathematics |
| Total Pages | : 0 |
| Release | : 1992 |
| Genre | : Chaotic behavior in systems |
| ISBN | : 9780070252035 |
| Author | : Flavio Lorenzelli |
| Publisher | : CRC Press |
| Total Pages | : 236 |
| Release | : 2003-09-02 |
| Genre | : Science |
| ISBN | : 0203214587 |
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.
| Author | : Florin Diacu |
| Publisher | : Princeton University Press |
| Total Pages | : 258 |
| Release | : 1999-03-28 |
| Genre | : Mathematics |
| ISBN | : 9780691005454 |
Celestial Encounters traces the history of attempts to solve the problem of celestial mechanics first posited in Isaac Newton's Principia in 1686. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it. 23 halftones. 64 line illustrations.
| Author | : Denny Gulick |
| Publisher | : CRC Press |
| Total Pages | : 390 |
| Release | : 2012-04-26 |
| Genre | : Mathematics |
| ISBN | : 1584885173 |
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.
| Author | : Stephanie Wodianka |
| Publisher | : transcript Verlag |
| Total Pages | : 253 |
| Release | : 2017-06-30 |
| Genre | : Social Science |
| ISBN | : 3839433894 |
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.
| Author | : Ralph Abraham |
| Publisher | : World Scientific |
| Total Pages | : 236 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9789812386472 |
This book is an authoritative and unique reference for the history of chaos theory, told by the pioneers themselves. It also provides an excellent historical introduction to the concepts. There are eleven contributions, and six of them are published here for the first time OCo two by Steve Smale, three by Yoshisuke Ueda, and one each by Ralph Abraham, Edward Lorenz, Christian Mira, Floris Takens, T Y Li and James A Yorke, and Otto E Rossler. Contents: On How I Got Started in Dynamical Systems 1959OCo1962 (S Smale); Finding a Horseshoe on the Beaches of Rio (S Smale); Strange Attractors and the Origin of Chaos (Y Ueda); My Encounter with Chaos (Y Ueda); Reflections on the Origin of the Broken-Egg Chaotic Attractor (Y Ueda); The Chaos Revolution: A Personal View (R Abraham); The Butterfly Effect (E Lorenz); I Gumowski and a Toulouse Research Group in the OC PrehistoricOCO Times of Chaotic Dynamics (C Mira); The Turbulence Paper of D Ruelle & F Takens (F Takens); Exploring Chaos on an Interval (T Y Li & J A Yorke); Chaos, Hyperchaos and the Double-Perspective (O E RAssler). Readership: Educators and university students of science and mathematics."
| Author | : Angelo Vulpiani |
| Publisher | : World Scientific |
| Total Pages | : 482 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 9814277665 |
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
| Author | : Joanne Wieland-Burston |
| Publisher | : Routledge |
| Total Pages | : 138 |
| Release | : 2015-06-18 |
| Genre | : Psychology |
| ISBN | : 1317404173 |
‘I don’t know what’s the matter with me – everything’s upside down; the whole world seems chaotic’ Chaos may erupt in our lives in many different ways – through death, divorce, conflict with family, friends or colleagues. It is a frightening and negative experience, destabilizing the individual and provoking feelings of insecurity. Originally published in English in 1992, the author, through her work as a Jungian analyst, frequently acted as a companion, support and guide to those whose lives were in chaotic turmoil. She describes how therapy helps people to meet chaos, to accept and see it in a different way – as a starting point for a new kind of order in their lives. This ‘organic’ order is better suited to their own personal needs and personality and provides the strong and flexible basis necessary to meet the chaos that belongs to life. Drawing upon the myths, tales and rites of ancient cultures, upon modern chaos theory, and upon her experience as an analyst the author shows the way through the chaos to a fuller, happier and more satisfying life.
| Author | : Constance Gillam |
| Publisher | : Entangled: Amara |
| Total Pages | : 287 |
| Release | : 2021-11-16 |
| Genre | : Fiction |
| ISBN | : 1682815943 |
What happens when a random hookup turns into the ultimate dilemma? Rashida Howard has never been a one-night-stand kind of woman, but she has good reason for making an exception with Elliott after meeting him in a bar. Cliché? Yes. Utterly amazing? Absolutely. Regrets? None. Elliott Quinn is a workaholic. The one night he decides to break his routine, he has an encounter with the woman of his dreams. But no matter how amazing they are together, work will always come first. Now they’re fighting on opposite sides of an ongoing battle between Elliott’s company and Rashida’s community. It’s turning their lives upside down and seriously complicating the chemistry between them. Neither will risk their integrity or their heart...until they uncover the one secret that will change the game entirely.
