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

07/19/2021

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by   Valerii Sopin, et al.

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For any 1-lipschitz ergodic map F: ℤ^k_p↦ℤ^k_p, k>1∈ℕ, there are 1-lipschitz ergodic map G: ℤ_p↦ℤ_p and two bijection H_k, T_k, P that G = H_k∘ T_k, P∘ F∘ H^-1_k and F = H^-1_k∘ T_k, P^-1∘ G∘ H_k.