Let   be an ergodic Markovian noise process with invariant measure π_ξ. Sufficient conditions are given for the ergodicity of the pair Markov process   arising from the nonlinear stochastic difference equation   on a manifold M and with f being at least a continuous map. An essential condition for ergodicity is the existence of a unique maximal invariant control set C for the associated control system   the support of π_ξ It is shown that under some further hypotheses involving compactness and weak stochastic controllability, the set C supp (π_ξ) is Harris recurrent for the pair process   and that the invariant measure on C supp (π_ξ) is unique and finite. Since geometric control theory is used to prove ergodicity, several results concerning control sets of discrete time dynamical systems are also given