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) 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. er, if M has the fixed point property, then a generic f ∈ C ( M , M ) generates uncountably many distinct copies of every possible adding machine.