Ergodic dynamical systems over the cartesian power of the ring of p-adic integers

For any 1-lipschitz ergodic map F: ? _p ^k ? ? _p ^k , k >1 ∈ ?, there are 1-lipschitz ergodic map G: ? _p ? ? _p and two bijections H _k , T _{k, P} that $G = H_k circ T_{k,P} circ F circ H_k^{ - 1} andF = H_k^{ - 1} circ T_{k,P - 1} circ G circ H_k $ .