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Ergodic dynamical systems over the Cartesian power of the ring of p-adic integers. (arXiv:2107.09059v1 [math.DS])

For any 1-lipschitz ergodic map $F:; mathbb{Z}^{k}_{p} mapsto
mathbb{Z}^{k}_{p},;k>1inmathbb{N},$ there are 1-lipschitz ergodic map $G:;
mathbb{Z}_{p} mapsto mathbb{Z}_{p}$ and two bijection $H_k$, $T_{k,;P}$
that $$G = H_{k} circ T_{k,;P}circ Fcirc H^{-1}_{k} text{ and } F =
H^{-1}_{k} circ T_{k,;P^{-1}}circ Gcirc H_{k}.$$