A measure of maximal entropy of the rational fraction on the Riemann sphere according to Arnaud Chéritat. It describes the distribution of preimages of almost all points.
Posts Tagged ‘pictures’
Consider the family of symmetric towel maps (the towel terminology is due to S. Newhouse):
This looks like a very natural generalization of quadratic interval maps, a step beyond the Viana maps of the form . These maps can also be understood as a coupling of two chaotic interval maps.
One would like to prove things like a two-dimensional version of Jakobson theorem. However little is known about these dynamics, except for their measures of maximal entropy which I was able to study using the entropy-expansion condition (for small enough ).
Now, let , and iterate a random point of forward….
or backward (chosing randomly between the preimages) at each step:
Nice pictures, aren’t they? A towel and its diffraction pattern 😉
More on this later, hopefully…
The Orsay campus has beautiful and diverse trees which take on gorgeous colors as can be guessed from the header picture (no post-processing, mind you!) taken in the fall of 2007 on the path betweeen the train station and the math dept.