Dynamics of the $p$-adic Shift and Applications

Details Dynamics of the $p$-adic Shift and Applications Dynamics of the $p$-adic Shift and Applications

2009-03-25

arxiv.org/abs/0903.4226v1

Discrete Contin. Dyn. Syst. 30 (2011), no. 1, 209-218

Mathematics

Dynamical Systems

15 pages, 1 figure

Scientific paper

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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