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    Topology and Dynamics of Chaos In Celebration of Robert Gilmore's 70th Birthday

    ISBN-10: 981443485X
    ISBN-13: 9789814434850
    Author(s): Christophe Letellier, Robert Gilmore, Universit� de Rouen Staff
    Description: The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included.The contents are mainly devoted to topology, the main field of Robert Gilmore's  More...
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    Publisher: World Scientific Publishing Co Pte Ltd
    Binding: Hardcover
    Pages: 364
    Size: 6.75" wide x 10.00" long x 1.00" tall
    Weight: 1.694
    Language: English

    The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included.The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists, Otto Rössler, René Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively.Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical — not necessarily widely known — contributions (about the different types of chaos introduced by Rössler and not just the "Rössler attractor"; Gumowski and Mira's contributions in electronics; Poincaré's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc.

    Preface
    Introduction to topological analysis
    Emergence of a Chaos Theory
    The peregrinations of Poincar�
    A Toulouse research group in the "prehistoric" times of chaotic dynamics
    Can we trust in numerical computations of chaotic solution of dynamical systems?
    Chaos hierarchy - A review, thirty years later
    Development of the Topology of Chaos
    The mathematics of Lorenz knots
    A braided view of a knotty story
    How topology came to chaos
    Reflections from the fourth dimension
    The symmetry of chaos
    Applications of Chaos Theory
    The shape of ocean color
    Low dimensional dynamics in biological motor patterns
    Minimal smooth chaotic flows
    The chaotic marriage of physics and financial economics
    Introduction of the sphere map with application to spin-torque nano-oscillators
    Robert Gilmore, a portrait
    Author Index
    Subject Index

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