Topology and Dynamics of Chaos (2013)

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 90s, 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 constributions in electronics ; Poincaré’s heritage in nonlinear dynamics, but also some recent applications in laser dynamics, biology, etc.

 Contents

• Introduction to the topological analysis by Christophe Letellier & Robert Gilmore
• The Peregrinations of Poincaré by Ralph Abraham
• A Toulouse research group in the « prehistoric » times of chaotic dynamics by Christian Mira
• Can we trust in numerical computations of chaotic solutions of dynamical systems ? by René Lozi
• Chaos Hierarchy. A review thirty years later by Otto E. Rössler & Christophe Letellier
• Lorenz Knots by Joan S. Birman
• A Braided View of a Knotty Story by Mario Natiello & Hernan Solari
• How topology came to chaos by Robert Gilmore
• Reflections from the fourth dimension by Marc Lefranc
• The symmetry of chaos by Christophe Letellier
• The shape of ocean color by Nicholas Tufillaro
• Low dimensional dynamics in biological motor patterns by Gabriel B. Mindlin
• Minimal smooth chaotic flows by Jean-Marc Malasoma
• The Chaotic Marriage of Physics and Financial Economics by Claire Gilmore
• Introduction of the sphere map with application to spin-torque nano-oscillators by Keith Gilmore & Robert Gilmore
• Robert Gilmore, a portrait by Hernan G. Solari

300 pp
May 2013
ISBN : 978-981-4434-85-0
Hardcover