03294cam a22002537i 4500001000700000003002100007005001700028008004100045020002900086040001600115082002100131111010800152245014300260260004300403300004100446490006800487504005100555505119000606520109201796650004202888650004502930700003602975700002903011135686ISI Library, Kolkata20150423143505.0130716s2013 njua b 111 0 eng d a9789814434850 (hardback) aISI Library00a514.74223bIn612 aInternational Workshop on "From Laser Dynamics to Topology of Chaos"d(28-30 Jun 2011 :cRouen, France)10aTopology and dynamics of chaos :bin celebration of Robert Gilmore's 70th birthday /c[edited by] Christophe Letellier and Robert Gilmore. aSingapore :bWorld Scientific,cc2013. ax, 351 p. :billustrations ;c26 cm.0 aWorld scientific series on nonlinear science ;vseries A, v 84. aIncludes bibliographical references and index. a1. Introduction to topological analysis / Christophe Letellier & Robert Gilmore --
2. The peregrinations of Poincare / R. Abraham --
3. A Toulouse research group in the "prehistoric" times of chaotic dynamics / Christian Mira --
4. Can we trust in numerical computations of chaotic solutions of dynamical systems? / Rene Lozi --
5. Chaos hierarchy --
a review, thirty years later / Otto E. Rossler & Christophe Letellier --
6. The mathematics of Lorenz knots / Joan S. Birman --
7. A braided view of a knotty story / Mario Natiello & Hernan Solari --
8. How topology came to chaos / Robert Gilmore --
9. Reflections from the fourth dimension / Marc Lefranc --
10. The symmetry of chaos / Christophe Letellier --
11. The shape of ocean color / Nicholas Tufillaro --
12. Low dimensional dynamics in biological motor patterns / Gabriel B. Mindlin --
13. Minimal smooth chaotic flows / Jean-Marc Malasoma --
14. The chaotic marriage of physics and financial economics / Claire Gilmore --
15. Introduction of the sphere map with application to spin-torque nano-oscillators / Keith Gilmore & Robert Gilmore --
16. Robert Gilmore, a portrait / Hernan G. Solari--
Author index--
Subject index. aThe 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 Rossler, Rene 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 Rossler and not just the "Rossler attractor "; Gumowski and Mira's contributions in electronics; Poincare's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc. 0aAttractors (Mathematics)vCongresses. 0aChaotic behavior in systemsvCongresses.1 aLetellier, Christophe,eeditor 1 aGilmore, Robert,eeditor