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’

## A measure of maximal entropy (by A. Chéritat)

Posted in Dynamics, tagged Dynamics, maximal entropy measure, pictures, smooth ergodic theory on December 3, 2009| Leave a Comment »

## Backward and Forward with the Towel Map

Posted in musings, tagged chaos, computer simulations, Dynamics, entropy, pictures, smooth ergodic theory, towel map on February 23, 2009| Leave a Comment »

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…

## Fall in Orsay

Posted in photo, tagged fall, orsay, pictures, ponds, trees on February 23, 2009| Leave a Comment »

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.