ON ERGODIC BEHAVIOR OF p-ADIC DYNAMICAL SYSTEMS
Matthias GundlachInstitut für Dynamische Systeme, Universität Bremen, Postfach 330440, 28334 Bremen, GermanyAndrei KhrennikovSchool of Mathematics and Systems Engineering, Växjö University, 35195, Växjö, SwedenKarl‐Olof LindahlSchool of Mathematics and Systems Engineering, Växjö University, 35195, Växjö, Sweden
2001en
ABI
Annotatsiya
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 will not have ergodicity on the unit circle, but on the circles around the point 1.
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