We investigate the dynamics of unimodal maps $f$ of the interval restrictedto the omega limit set $X$ of the critical point for cases where $X$ is aCantor set.In particular, many cases where $X$ isa measure attractor of $f$ are included. We give two classes of examples ofsuch maps, both generalizing unimodal Fibonacci maps [LM,BKNS]. In allcases $f_{|X}$ is a continuous factor of a generalized odometer (an addingmachine-like dynamical system), and at the same time $f_{|X}$ factors ontoan irrational circle rotation. In some of the examples we obtain irrationalrotations on more complicated groups as factors.