Ebook: Nonlinear Evolution and Chaotic Phenomena

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.

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Content:
Front Matter....Pages i-ix
Conference Summary....Pages 1-3
Complicated Objects on Regular Trees....Pages 5-24
Renormalization Group Methods for Circle Mappings....Pages 25-36
Phase Transitions on Strange Sets....Pages 37-54
Stochastic Perturbations of the Invariant Measure of Some Hyperbolic Dynamical Systems....Pages 55-69
Fixed Points of Composition Operators....Pages 71-100
Differentiable Structures on Fractal Like Sets, Determined by Intrinsic Scaling Functions on Dual Cantor Sets....Pages 101-110
Painlev? Property and Integrability....Pages 111-119
Nekhoroshev-Like Results for Hamiltonian Dynamical Systems....Pages 121-146
Relaxation Times and the Foundations of Classical Statistical Mechanics in the Light of Modern Perturbation Theory....Pages 147-159
Relevance of Exponentially Large Time Scales in Practical Applications: Effective Fractal Dimensions in Conservative Dynamical Systems....Pages 161-170
Numerical Results from Truncated Navier-Stokes Equations....Pages 171-171
A Simple and Compact Presentation of Birkhoff Series....Pages 173-183
Two Lectures on Chaotic Dynamics in the Solar System....Pages 185-187
Quantum Chaology of Energy Levels Notes Based on Lectures by Michael Berry....Pages 189-196
Quantum Mechanics and Chaos....Pages 197-212
Dynamics of Automata, Spin Glasses and Neural Network Models....Pages 213-244
On the Weakly Coupled Lorentz Gas....Pages 245-253
Dynamical System Describing the Low Temperature Phase of a Driven Lattice Gas....Pages 255-267
Computing Bounds on Critical Indices....Pages 269-277
A Thermodynamic Active System in Regular and Chaotic Motion....Pages 279-288
Experiment and Theory of the Classically Chaotic Motion of the Driven Bound Electron....Pages 289-300
Shil’nikov Chaos in Lasers....Pages 301-312
Recent Results of Experiments with Saffman-Taylor Flow....Pages 313-317
Instabilites and Chaos in Rotating Fluid....Pages 319-326
From Chaos to Turbulence in an Helium Experiment....Pages 327-327
Complex Dynamics in Experiments on a Chemical Reaction....Pages 329-329
Back Matter....Pages 331-337

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Content:
Front Matter....Pages i-ix
Conference Summary....Pages 1-3
Complicated Objects on Regular Trees....Pages 5-24
Renormalization Group Methods for Circle Mappings....Pages 25-36
Phase Transitions on Strange Sets....Pages 37-54
Stochastic Perturbations of the Invariant Measure of Some Hyperbolic Dynamical Systems....Pages 55-69
Fixed Points of Composition Operators....Pages 71-100
Differentiable Structures on Fractal Like Sets, Determined by Intrinsic Scaling Functions on Dual Cantor Sets....Pages 101-110
Painlev? Property and Integrability....Pages 111-119
Nekhoroshev-Like Results for Hamiltonian Dynamical Systems....Pages 121-146
Relaxation Times and the Foundations of Classical Statistical Mechanics in the Light of Modern Perturbation Theory....Pages 147-159
Relevance of Exponentially Large Time Scales in Practical Applications: Effective Fractal Dimensions in Conservative Dynamical Systems....Pages 161-170
Numerical Results from Truncated Navier-Stokes Equations....Pages 171-171
A Simple and Compact Presentation of Birkhoff Series....Pages 173-183
Two Lectures on Chaotic Dynamics in the Solar System....Pages 185-187
Quantum Chaology of Energy Levels Notes Based on Lectures by Michael Berry....Pages 189-196
Quantum Mechanics and Chaos....Pages 197-212
Dynamics of Automata, Spin Glasses and Neural Network Models....Pages 213-244
On the Weakly Coupled Lorentz Gas....Pages 245-253
Dynamical System Describing the Low Temperature Phase of a Driven Lattice Gas....Pages 255-267
Computing Bounds on Critical Indices....Pages 269-277
A Thermodynamic Active System in Regular and Chaotic Motion....Pages 279-288
Experiment and Theory of the Classically Chaotic Motion of the Driven Bound Electron....Pages 289-300
Shil’nikov Chaos in Lasers....Pages 301-312
Recent Results of Experiments with Saffman-Taylor Flow....Pages 313-317
Instabilites and Chaos in Rotating Fluid....Pages 319-326
From Chaos to Turbulence in an Helium Experiment....Pages 327-327
Complex Dynamics in Experiments on a Chemical Reaction....Pages 329-329
Back Matter....Pages 331-337
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