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Author: Joachim Peinke Publisher: Springer Science & Business Media ISBN: 3642776256 Category : Science Languages : en Pages : 298
Book Description
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: Joachim Peinke Publisher: Springer Science & Business Media ISBN: 3642776256 Category : Science Languages : en Pages : 298
Book Description
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: Flavio Lorenzelli Publisher: CRC Press ISBN: 0203214587 Category : Science Languages : en Pages : 236
Book Description
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 ISBN: 9780691005454 Category : Mathematics Languages : en Pages : 258
Book Description
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 ISBN: 1584885173 Category : Mathematics Languages : en Pages : 390
Book Description
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 ISBN: 3839433894 Category : Social Science Languages : en Pages : 253
Book Description
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: Tom O'Neill Publisher: Little, Brown ISBN: 0316477575 Category : True Crime Languages : en Pages : 500
Book Description
A journalist's twenty-year fascination with the Manson murders leads to "gobsmacking" (The Ringer) new revelations about the FBI's involvement in this "kaleidoscopic" (The New York Times) reassessment of an infamous case in American history. Over two grim nights in Los Angeles, the young followers of Charles Manson murdered seven people, including the actress Sharon Tate, then eight months pregnant. With no mercy and seemingly no motive, the Manson Family followed their leader's every order -- their crimes lit a flame of paranoia across the nation, spelling the end of the sixties. Manson became one of history's most infamous criminals, his name forever attached to an era when charlatans mixed with prodigies, free love was as possible as brainwashing, and utopia -- or dystopia -- was just an acid trip away. Twenty years ago, when journalist Tom O'Neill was reporting a magazine piece about the murders, he worried there was nothing new to say. Then he unearthed shocking evidence of a cover-up behind the "official" story, including police carelessness, legal misconduct, and potential surveillance by intelligence agents. When a tense interview with Vincent Bugliosi -- prosecutor of the Manson Family and author of Helter Skelter -- turned a friendly source into a nemesis, O'Neill knew he was onto something. But every discovery brought more questions: Who were Manson's real friends in Hollywood, and how far would they go to hide their ties? Why didn't law enforcement, including Manson's own parole officer, act on their many chances to stop him? And how did Manson -- an illiterate ex-con -- turn a group of peaceful hippies into remorseless killers? O'Neill's quest for the truth led him from reclusive celebrities to seasoned spies, from San Francisco's summer of love to the shadowy sites of the CIA's mind-control experiments, on a trail rife with shady cover-ups and suspicious coincidences. The product of two decades of reporting, hundreds of new interviews, and dozens of never-before-seen documents from the LAPD, the FBI, and the CIA, Chaos mounts an argument that could be, according to Los Angeles Deputy District Attorney Steven Kay, strong enough to overturn the verdicts on the Manson murders. This is a book that overturns our understanding of a pivotal time in American history.
Author: Ralph Abraham Publisher: World Scientific ISBN: 9789812386472 Category : Mathematics Languages : en Pages : 236
Book Description
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: Joanne Wieland-Burston Publisher: Routledge ISBN: 1317404173 Category : Psychology Languages : en Pages : 138
Book Description
‘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: Angelo Vulpiani Publisher: World Scientific ISBN: 9814277665 Category : Mathematics Languages : en Pages : 482
Book Description
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: Joachim Peinke
Author: Joachim Peinke
Author: Denny Gulick
Author: Flavio Lorenzelli
Author: Florin Diacu
Author: Denny Gulick
Author: Stephanie Wodianka
Author: Tom O'Neill
Author: Ralph Abraham
Author: Joanne Wieland-Burston
Author: Angelo Vulpiani