On Ergodic Behavior of p-adic dynamical systems
By M. Gundlach, A. Khrennikov, Karl-Olof Lindahl. 2001
54 citations recorded by the source corpus.
Monomial mappings, x ↦ xn, 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.
Subfields: Computational Theory and Mathematics, Mathematical Physics, Physiology
View Paper: https://www.semanticscholar.org/paper/49e3363454a134ed494b34add7fe157cc9c01bbf
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Citations in the corpus
- Ergodic Transformations in the Space of p‐Adic Integers (2006, methodology): “Earlier in [15] and [14] ergodicity of monomial mappings z 7→ z on spheres Sp−r(1) of a radius p −r with a center at 1 was studied: It was shown that for odd p and r > 1 the mapping is ergodic iff l is a generator of the group (Z/p(2)Z).”
- ON MINIMAL DECOMPOSITION OF p-ADIC POLYNOMIAL DYNAMICAL SYSTEMS (2010, background): “n the abovedecomposition are called minimal components. Recently the theory of Non-Archimedean, in particular of p-adic, dynamical systems has been intensively developed ([6, 7, 8], [13], [14], [16], [17], [18], [19, 20], [24], [26], [30], [33], [37], [39]). See also the monographes [5], [25], [36] ”