[en] 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.
Disciplines :
Mathematics
Author, co-author :
Simons, Laurent ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Nicolay, Samuel ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
About the Regularity of Cantor's Bijection
Alternative titles :
[fr] A propos de la régularité de la bijection de Cantor
