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arXiv · 0806.0260

On ergodic behavior of $p$-adic dynamical systems

Matthias Gundlach·Andrei Khrennikov·Karl-Olof Lindahl
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Abstract

Monomial mappings, $x\mapsto x^n$, are topologically transitive and ergodic with respect to Haar measure on the unit circle in the complex plane. In this paper we obtain an anologous result for monomial dynamical systems over $p-$adic numbers. The process is, however, not straightforward. The result will depend on the natural number $n$. Moreover, in the $p-$adic case we never have ergodicity on the unit circle, but on the circles around the point 1.

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Matthias Gundlach, Andrei Khrennikov, Karl-Olof Lindahl. 2008-06-02. On ergodic behavior of $p$-adic dynamical systems. https://arxiv.org/abs/0806.0260

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