Ubiquity of odometers in topological dynamical systems

Let M be the Cantor space or an n-manifold with C(M,M) the set of continuous self-maps of M. We prove the following:(1)There is a residual set of points (x,f) in M×C(M,M) all of which generate as their ω-limit set a particular, unique adding machine.(2)Moreover, if M has the fixed point property, then a generic f∈C(M,M) generates uncountably many distinct copies of every possible adding machine.