By Christophe Letellier,Robert Gilmore

The booklet surveys how chaotic behaviors might be defined with topological instruments and the way this strategy happened in chaos thought. a few sleek purposes are included.

The contents are in most cases dedicated to topology, the most box of Robert Gilmore's works in dynamical structures. They contain a evaluate at the topological research of chaotic dynamics, works performed some time past in addition to the very most modern concerns. lots of the members who released through the 90's, together with the very recognized scientists Otto Rössler, René Lozi and Joan Birman, have made an important effect on chaos thought, discrete chaos, and knot idea, respectively.

Very few books hide the topological method for investigating nonlinear dynamical platforms. the current ebook will supply not just a few old — no longer inevitably well known — contributions (about the different sorts of chaos brought through Rössler and never simply the “Rössler attractor”; Gumowski and Mira's contributions in electronics; Poincaré's historical past in nonlinear dynamics) but additionally a few contemporary functions in laser dynamics, biology, etc.

Contents:

  • Introduction to Topological research (Christophe Letellier & Robert Gilmore)
  • Emergence of a Chaos Theory:
    • The Peregrinations of Poincaré (R Abraham)
    • A Toulouse examine staff within the “Prehistoric” occasions of Chaotic Dynamics (Christian Mira)
    • Can We belief in Numerical Computations of Chaotic recommendations of Dynamical structures? (René Lozi)
    • Chaos Hierarchy — A evaluate, Thirty Years Later (Otto E Rössler & Christophe Letellier)
  • Development of the Topology of Chaos:
    • The arithmetic of Lorenz Knots (Joan S Birman)
    • A Braided View of a Knotty tale (Mario Natiello & Hernán Solari)
    • How Topology got here to Chaos (Robert Gilmore)
    • Reflections From the Fourth size (Marc Lefranc)
    • The Symmetry of Chaos (Christophe Letellier)
  • Applications of Chaos Theory:
    • The form of Ocean colour (Nicholas Tufillaro)
    • Low Dimensional Dynamics in organic Motor styles (Gabriel B Mindlin)
    • Minimal delicate Chaotic Flows (Jean-Marc Malasoma)
    • The Chaotic Marriage of Physics and fiscal Economics (Claire Gilmore)
    • Introduction of the field Map with software to Spin-Torque Nano-Oscillators (Keith Gilmore & Robert Gilmore)
    • Robert Gilmore, a Portrait (Hernán G Solari)

Readership: Graduate scholars and researchers attracted to topological research of nonlinear dynamical structures generating chaotic attractors.

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