## by Carl D. Murray and Stanley F. Dermott

# Chapter 9

# Chaos and Long-Term Evolution

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- Structure of the Solar System
- The Two-Body Problem
- The Restricted Three-Body Problem
- Tides, Rotation and Shape
- Spin-Orbit Coupling
- The Disturbing Function
- Secular Perturbations
- Resonant Perturbations
**CHAOS AND LONG-TERM EVOLUTION**
**Introduction**
**Sensitive dependence on initial conditions**
**Regular and chaotic orbits**
**The Poincaré surface of section**
**Regular orbits**
**Chaotic orbits**
**The Lyapounov characteristic exponent**

**Chaos in the circular restricted problem**
**Algebraic mappings**
**The standard map**
**Resonance maps**
**Encounter maps**
*N*-body maps

**Separatrices and resonance overlap**
**The rotation of Hyperion**
**The Kirkwood gaps**
**Resonant structure of the asteroid belt**
**The 3:1 resonance**
**Other resonances**

**The Neptune-Pluto system**
**The stability of the solar system**
**Exercises**

- Planetary Rings

- Appendix - Solar System Data
- Appendix - Expansion of the Disturbing Function
- References (PDF)

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Table of Contents

Copyright © 1999-2006 by Carl D. Murray

Last modified on 8 September 2006

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