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Measuring the Preservation and Ergodicity of 1-Lipschitz Functions on the Ring of 3-Adic Integers in Terms of Coordinate Functions

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Abstract

Necessary and sufficient conditions are given under which \(1\)-Lipschitz function \(f(x)\) preserves the Haar measure on the ring of \(3\)-adic integers \({\mathbb{Z}}_{3}\); moreover, necessary and sufficient conditions are given under which \(f(x)\) is ergodic on \({\mathbb{Z}}_{3}\).

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REFERENCES

  1. V. Anashin and A. Khrennikov, Applied Algebraic Dynamics, De Gruyter Expositions in Mathematics, Vol. 49 (Walter De Gruyter, Berlin, 2009). https://doi.org/10.1515/9783110203011

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    A. Lopez Perez

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  1. A. Lopez Perez
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Correspondence to A. Lopez Perez.

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Translated by I. Tselishcheva

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Lopez Perez, A. Measuring the Preservation and Ergodicity of 1-Lipschitz Functions on the Ring of 3-Adic Integers in Terms of Coordinate Functions. MoscowUniv.Comput.Math.Cybern. 46, 89–92 (2022). https://doi.org/10.3103/S0278641922020066

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  • DOI: https://doi.org/10.3103/S0278641922020066

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