Period Doubling Exercise

In this exercise, we use scaling and renormalization--group methods to study the onset of chaos. There are several routes by which a dynamical system can start exhibiting chaotic motion: we study the period doubling cascade, first extensively investigated by Feigenbaum.

• Period Doubling Exercise.
• Brief notes on universality, fractal dimensions, and the renormalization group (also ppt).
• Python:
  • Logistic iteration hints (download first)
  • Logistic iteration answer and demo
  • Hints file
  • Answer and demo
  • Python nanotutorials
  • Starting up a new Python project under Linux
  • Python setup info

Related Exercises

• Invariant Measures
• Chaos and Lyapunov Exponents
• Fractal Dimensions

Links

• Course Web Page
• Book Web Page

Last modified: August 24, 2006

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).