On measure-preserving functions over ℤ3
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This paper is devoted to (discrete) p-adic dynamical systems, an important domain of algebraic and arithmetic dynamics –, –. 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 . 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 . 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.
Key wordsmeasure-preserving generalized polynomial van der Put basis 3-adic integers
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