Geodesic
Ergodic dynamical systems over the cartesian power of the ring of $2$-adic integers
Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 27-36.

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It is proved that, for any $1$-lipschitz ergodic map $F\colon\mathbb Z^k_2\mapsto\mathbb Z^k_2$, where $k>1$ and $k\in\mathbb N,$ there are $1$-lipschitz ergodic map $G\colon\mathbb Z_2\mapsto\mathbb Z_2$ and two bijections $H_k$, $T_{k,P}$ such that $G=H_k\circ T_{k,P}\circ F\circ H^{-1}_k$ and $F=H^{-1}_k\circ T_{k,P^{-1}}\circ G\circ H_k$.
Keywords: ergodic, $1$-lipschitz measure-preserving $p$-adic functions, $p$-adic analysis, cartesian product, T-functions. 
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V. V. Sopin. Ergodic dynamical systems over the cartesian power of the ring of $2$-adic integers. Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 27-36. http://geodesic.mathdoc.fr/item/PDM_2015_1_a2/

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