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Graphical evolution of the arnold web: from order to chaos
1Observatoire de Nice, Boulevard de l'Observatoire, Boite Postale 4229, 06304 Nice Cedex 4, France.
Science (New York, N.Y.)
|September 23, 2000
Summary
This study visualizes the Arnold web, revealing how dynamical system stability transitions from Nekhoroshev to Chirikov regimes. This graphical representation aids understanding of chaotic transport in physical systems.
Area of Science:
- Dynamical systems theory
- Statistical mechanics
- Astrophysics
Background:
- The Arnold web describes resonance structures in quasi-integrable dynamical systems.
- Understanding these structures is key to predicting system stability.
- Previous methods lacked direct ties to orbital dynamics.
Purpose of the Study:
- To graphically represent the evolution of the Arnold web.
- To illustrate the transition between stability regimes.
- To provide a model for chaotic transport phenomena.
Main Methods:
- Development of an original numerical method based on orbit dynamics.
- Selection of a specific model system for analysis.
- Graphical visualization of resonance set evolution.
Main Results:
- The study successfully depicts the Arnold web's structural changes.
- The transition from Nekhoroshev to Chirikov stability regimes is demonstrated.
- The model system exhibits generic chaotic transport behaviors.
Conclusions:
- The graphical Arnold web representation offers new insights into dynamical system stability.
- The observed transition is a fundamental phenomenon applicable to various physical processes.
- This work provides a foundation for studying chaotic transport in systems like the asteroid belt.
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