Continued Fractions and Chaos

Robert M. Corless
Dept. Applied Math
University of Western Ontario
London, Ontario
Canada

• Contents
• Introduction
• Summary of Classical Results
  • The Gauss Map.
• Dynamical Systems Terminology
• Classical Results Interpreted in Dynamical Systems Terminology
  • Periodic and Fixed Points of the Gauss Map
  • Aperiodic Points
  • Lyapunov Exponents
    • Remark.
  • Ergodic Results
• The Floating-Point Gauss Map
  • Orbits under are close to orbits under G.
  • A new method for calculating .
    • Remarks.
• Conclusion
  • Acknowledgements
• References
• About this document ...