Topology and Dynamics of Chaos

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 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 (Christophe Letellier & Robert Gilmore)
• The Peregrinations of Poincaré (Ralph 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 & Christophe Letellier)
• Lorenz Knots (Joan S. Birman)
• A Braided View of a Knotty Story (Mario Natiello & Hernan 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 & Robert Gilmore)
• Robert Gilmore, a portrait (Hernan G. Solari)

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