Nonlinear Evolution and Chaotic Phenomena

1. Front Matter

   Pages i-ix

   PDF

2. Introduction

   1. Conference Summary

      • Giovanni Gallavotti

      Pages 1-3

3. Chaotic Maps

   1. Complicated Objects on Regular Trees

      • Mitchell Feigenbaum

      Pages 5-24

   2. Renormalization Group Methods for Circle Mappings

      • Oscar E. Lariford III

      Pages 25-36

   3. Phase Transitions on Strange Sets

      • Predrag Cvitanović

      Pages 37-54

   4. Stochastic Perturbations of the Invariant Measure of Some Hyperbolic Dynamical Systems

      • Pierre Collet

      Pages 55-69

   5. Fixed Points of Composition Operators

      • Henri Epstein

      Pages 71-100

   6. Differentiable Structures on Fractal Like Sets, Determined by Intrinsic Scaling Functions on Dual Cantor Sets

      • Dennis Sullivan

      Pages 101-110

4. Classical Mechanics-Particles and Fluids

   1. Painlevé Property and Integrability

      • Eric D. Siggia

      Pages 111-119

   2. Nekhoroshev-Like Results for Hamiltonian Dynamical Systems

      • Giancarlo Benettin

      Pages 121-146

   3. Relaxation Times and the Foundations of Classical Statistical Mechanics in the Light of Modern Perturbation Theory

      • Luigi Galgani

      Pages 147-159

   4. Relevance of Exponentially Large Time Scales in Practical Applications: Effective Fractal Dimensions in Conservative Dynamical Systems

      • Antonio Giorgilli

      Pages 161-170

   5. Numerical Results from Truncated Navier-Stokes Equations

      • V. Franceschini

      Pages 171-171

   6. A Simple and Compact Presentation of Birkhoff Series

      • Michel Vittot

      Pages 173-183

   7. Two Lectures on Chaotic Dynamics in the Solar System

      • Jack Wisdom

      Pages 185-187

5. Quantum Chaos

   1. Quantum Chaology of Energy Levels Notes Based on Lectures by Michael Berry

      • Jonathan Keating, Raul Mondragon

      Pages 189-196

   2. Quantum Mechanics and Chaos

      • Giulio Casati

      Pages 197-212

6. Statistical Mechanics

   1. Dynamics of Automata, Spin Glasses and Neural Network Models

      • B. Derrida

      Pages 213-244

   2. On the Weakly Coupled Lorentz Gas

      • Detlef Dürr

      Pages 245-253

   3. Dynamical System Describing the Low Temperature Phase of a Driven Lattice Gas

      • Joachim Krug, Herbert Spohn

      Pages 255-267

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.

• Renormalization group
• chaos
• dynamical systems
• dynamics
• electron
• energy
• experiment
• mechanics
• particles
• quantum mechanics
• solar system
• spin
• statistical mechanics
• turbulence

• Accademia dei Lincei, Centro Linceo Interdisciplinare “B. Segre”, Rome, Italy

  Giovanni Gallavotti

• Virginia Polytechnic Institute and State University, Blacksburg, USA

  Paul F. Zweifel

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