We have five exercises on discrete maps. Before working on this one, you should first do the Logistic Map exercises.
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
Science: You will learn about Chaos, discrete maps, and fractal dimensions.
Computation: You will learn about iterative algorithms, and techniques to explore asymptotic behaviors.
- Download and have a quick glance at Brief notes on
universality, fractal dimensions, and the renormalization group.
- Download the file ChaosLyapunovHints.py and rename it "ChaosLyapunov.py".
- Open this file in a text editor (kate or emacs -- we recommend against using kedit) or load it into the IPython dashboard (started with ipython notebook --pylab inline.
- Open a terminal window, move to the correct directory and start ipython, or click on the notebook in the dashboard. You will find it convenient to start python with the --pylab flag -- ie type ipython --pylab or ipython notebook --pylab.
- Follow the directions in Period Doubling Exercise.