Based on the Schweiger’s smooth fibered approach and the related Bernoulli shift transformation scheme, we prove the ergodicity of the two-dimensional Boole-type transformations. New multidimensional Boole-type transformations invariant with respect to the Lebesgue measure and their ergodicity properties are also discussed.
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Dedicated to the commemoration of untimely passed away outstanding Ukrainian mathematician Prof. A. M. Samoilenko
Published in Neliniini Kolyvannya, Vol. 26, No. 1, pp. 113–131, January–March, 2023.
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Prykarpatski, A.K., Balinsky, A.A. The Two-Dimensional Boole-Type Transform and its Ergodicity. J Math Sci 278, 1055–1076 (2024). https://doi.org/10.1007/s10958-024-06977-6
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DOI: https://doi.org/10.1007/s10958-024-06977-6