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manneville-pomeau

A collection of Python scripts and tex files relative to the family of Manneville-Pomeau interval maps.

Some or all of these are used in my undergraduate final year MMath project on intermittency in dynamical systems, under supervision by Dr Mike Todd.

I'm using the definition of the Manneville-Pomeau map from [LSV99], where it is defined as a map from [0,1] to itself given by:

for a parameter alpha strictly greater than 0.

A number of standard computations are of interest:

  • Finding this map's Markov partition
  • Inducing this map on the interval [1/2, 1] (in order to prove it is an expanding map, for example)
  • Calculating the size of the return time tails

My final year project provides and illustrates these computations analytically and numerically in a broad overview of the variety of ergodic results that can be proven for a canonical map like this one.