Thomae's function and the space of ergodic measures

Abstract

We study the space of ergodic measures of the map $$f:{\mathbb{T}}^2\to {\mathbb{T}}^2,f(x,y)=(x,x+y)(\text{mod}1),$$ and show that its structure is similar to the graph of Thomae's function.

6 pages, 2 figures