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