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On measure-preserving functions over ℤ3

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Abstract

This paper is devoted to (discrete) p-adic dynamical systems, an important domain of algebraic and arithmetic dynamics [31]–[41], [5]–[8]. In this note we study properties of measurepreserving dynamical systems in the case p = 3. This case differs crucially from the case p = 2. The latter was studied in the very detail in [43]. We state results on all compatible functions which preserve measure on the space of 3-adic integers, using previous work of A. Khrennikov and author of present paper, see [24]. To illustrate one of the obtained theorems we describe conditions for the 3-adic generalized polynomial to be measure-preserving on ℤ3. The generalized polynomials with integral coefficients were studied in [17, 33] and represent an important class of T-functions. In turn, it is well known that T-functions are well-used to create secure and efficient stream ciphers, pseudorandom number generators.

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  1. International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, School of Computer Science, Physics and Mathematics, Linnaeus University, 35195, Vaxjo, Sweden

    E. Yurova

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Yurova, E. On measure-preserving functions over ℤ3 . P-Adic Num Ultrametr Anal Appl 4, 326–335 (2012). https://doi.org/10.1134/S2070046612040061

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