|aWorld scientific series on nonlinear science, Series A,|x1793-1010 ;|vvolume 84.
|aIncludes bibliographical references and index.
|aIntroduction to topological analysis / Christophe Letellier and Robert Gilmore -- The peregrinations of Poincaré / R. Abraham -- A Toulouse research group in the "prehistoric" times of chaotic dynamics / Christian Mira -- Can we trust in numerical computations of chaotic solutions of dynamical systems? / René Lozi -- Chaos hierarchy - a review, thirty years later / Otto E. ̈Rössler and Christophe Letellier -- The mathematics of Lorenz knots / Joan S. Birman -- A braided view of a knotty story / Mario Natiello and Hernán Solari -- How topology came to chaos / Robert Gilmore -- Reflections from the fourth dimension / Marc Lefranc -- The symmetry of chaos / Christophe Letellier -- The shape of ocean color / Nicholas Tufillaro -- Low Dimensional dynamics in biological motor patterns / Gabriel B. Mindlin -- Minimal smooth chaotic flows / Jean-Marc Malasoma -- The chaotic marriage of physics and financial economics / Claire Gilmore -- Introduction of the sphere map with application to spin-torque nano-oscillators / Keith Gilmore and Robert Gilmore -- Robert Gilmore, a portrait / Hernán G. Solari.
|aChaotic behavior in systems|vCongresses.
|aLetellier, Christophe,|eeditor of compilation.
|aGilmore, Robert,|d1941-|ehonouree,|eeditor of compilation.
內容簡介top Topology and Dynamics of Chaos 簡介 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 R飉sler, Ren?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 R飉sler and not just the 飉sler attractor? Gumowski and Mira's constributions in electronics; Poincar?s heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc.