Figure 1.

Invariant measures of the generalized Bernoulli map $f_{\beta }$ for $\beta =\frac{6}{5},\frac{5}{4},\frac{4}{3},\frac{3}{2}$. These are normalized so that $h_{\beta }(1)=1$ (which corresponds to $C=1$ in Equation (1)). They are not as smooth as these graphs make them appear.