Abstract
Monomial mappings, x ↦ 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 analogous 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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Khrennikov, A., Lindahl, KO., Gundlach, M. (2002). Ergodicity in the p-adic Framework. In: Albeverio, S., Elander, N., Everitt, W.N., Kurasov, P. (eds) Operator Methods in Ordinary and Partial Differential Equations. Operator Theory: Advances and Applications, vol 132. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8219-4_19
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DOI: https://doi.org/10.1007/978-3-0348-8219-4_19
Publisher Name: Birkhäuser, Basel
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