Dynamics of the $p$-adic Shift and Applications

We present a novel way of realizing the Bernoulli shift on $p$ symbols on the $p$-adic integers, where $p$ is a prime. By showing that suitably small perturbations of the shift are still Bernoulli we find many "nice" maps, such as polynomials on $\mathbb Z_p$, that are isomorphic to the (noninvertible) Bernoulli shift.

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