A propos de la régularité de la bijection de Cantor

In 1878, Cantor proved that there exists a one-to-one correspondence between the points of the unit line segment [0,1] and the points of the unit square [0,1]². Since this application is defined via continued fractions, it is very hard to have any intuition about its smoothness. In this talk, we explore the regularity and the fractal nature of Cantor's bijection, using some notions concerning the metric theory and the ergodic theory of continued fractions. This talk is based on a joint work with S. Nicolay