Ergodic Transformations in the Space of p‐Adic Integers

By Vladimir Anashin. 2006

84 citations recorded by the source corpus.

Let L1 be the set of all mappings f : Zp → Zp of the space of all p‐adic integers Zp into itself that satisfy Lipschitz condition with a constant 1. We prove that the mapping f ∈ L1 is ergodic with respect to the normalized Haar measure on Zp if and only if f induces a single cycle permutation on each residue ring Z/pkZ modulo pk, for all k = 1, 2, 3, …. The multivariate case, as well as measure‐preserving mappings, are considered also.Results of the paper in a combination with earlier results of the author give explicit description of ergodic mappings from L1. This characterization is complete for p = 2.As an application we obtain a characterization of polynomials (and certain locally analytic functions) that induce ergodic transformations of p‐adic spheres. The latter result implies a solution of a problem due to A. Khrennikov about the ergodicity of a perturbed monomial mapping on a sphere.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/611de13439eb5cc2b1837eaf29c16b67c827c084

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Mingtian Li
2. Dan Zhou
3. Jia-Yan Yao
4. A. Fan
5. Lingmin Liao

In Mathematical Physics

1. Lingmin Liao
2. A. Fan
3. Mingtian Li
4. Dan Zhou
5. Jia-Yan Yao
6. De-Jun Feng
7. Daniel Thompson

Citations in the corpus

• Strict ergodicity of affine p-adic dynamical systems on Zp (2007, methodology): “9 in [3] may be deduced from our proofs and the Anashin’s general criterion.”
• ON MINIMAL DECOMPOSITION OF p-ADIC POLYNOMIAL DYNAMICAL SYSTEMS (2010, background): “If v2(t) ≤ 1, then 1 + 4Z2 is of type II-[v2(t) + 2].”