Coupled rotations and snow falling on cedars
Also appears in collections : The Fields Medallists, Fields medallists - 1998, Exposés de recherche
We study cascades of bifurcations in a simple family of maps on the circle, and connect this behavior to the geometry of an absolute period leaf in genus $2$. The presentation includes pictures of an exotic foliation of the upper half plane, computed with the aid of the Möller-Zagier formula.