Nonlinear Evolution and Chaotic Phenomena: (176 NATO Science Series B:)

This volume represents the proceedings of a NATO Advanced Study Institute held at Noto, Sicily June 8-19, 1987. The director was Giovanni Gallavotti, Roma, with co-directors Marcello Anile, Catania and P. F. Zweifel, Virginia Tech. Other members of the scientific organizing committee included Mitchell Feigenbaum, Rockefeller University and David Ruelle, IHES. The attendance at the school consisted of 23 invited speakers and approximately 80 "students", the term student being in quotation marks because many of them were of post-doctoral or even professorial status, although there were also a goodly number of actual graduate students in attendance also. Because of the disparate background of these "students", it was felt advisable to include at the conference special tutorials each afternoon, in which the contents of the morning's lectures were reviewed and clarified as necessary. These tutorials, organized by Gallavotti, involved various of the speakers, organizers, and other senior members of the school, and contributed in no little way to the overall success of the school. The organizers of the school would like to take this opportunity to thank all of those who assisted in these sessions, and to assure them that the results were definitely worth the effort. Also contributing to the success of the school were a number of contributed papers, presented during the course of the afternoon tutorials. Three of those papers are included in these proceedings; they are the papers of DiFrancesco; Gallimbeni, Miari and Sertorio (presented by Sertorio); and Vittot.

Table of Contents:
Conference Summary.- Chaotic Maps.- Complicated Objects on Regular Trees.- Renormalization Group Methods for Circle Mappings.- Phase Transitions on Strange Sets.- Stochastic Perturbations of the Invariant Measure of Some Hyperbolic Dynamical Systems.- Fixed Points of Composition Operators.- Differentiable Structures on Fractal Like Sets, Determined by Intrinsic Scaling Functions on Dual Cantor Sets.- Classical Mechanics-Particles and Fluids.- Painlevé: Property and Integrability.- Nekhoroshev-like Results for Hamiltonian Dynamical Systems.- Relaxation Times and the Foundations of Classical Statistical Mechanics in the Light of Modern Perturbation Theory.- Relevance of Exponentially Large Time Scales in Practical Applications: Effective Fractal Dimensions in Conservative Dynamical Systems.- Numerical Results from Truncated Navier-Stokes Equations (Summary).- A Simple and Compact Presentation of Birkhoff Series.- Two Lectures on Chaotic Dynamics in the Solar System.- Quantum Chaos.- Quantum Chaology of Energy Levels; Notes Based on Lectures by Michael Berry.- Quantum Mechanics and Chaos.- Statistical Mechanics.- Dynamics of Automota, Spin Glasses and Neural Network Models.- On the Weakly Coupled Lorentz Gas.- Dynamical System Describing the Low Temperature Phase of a Driven Lattice Gas.- Computing Bounds on Critical Indices.- A Thermodynamic Active System in Regular and Chaotic Motion.- Experiments.- Experiment and Theory of the Classically Chaotic Motion of the Bound Electron.- Shil’nikov Chaos in Lasers.- Recent Results of Experiments with Staffman-Taylor Flow.- Instabilities and Chaos in Rotating Fluids.- From Chaos to Turbulence in an Helium Experiment (Summary).- Complex Dynamics in Experiments on a Chemical Reaction (Summary).- Addenda.- Additional ContributedSeminars.- Contributors.