Memić, Nacima Notes on ergodic \(2\)-adic transformations. (English) Zbl 1458.37111 \(p\)-Adic Numbers Ultrametric Anal. Appl. 12, No. 4, 297-309 (2020). Summary: In this work we provide a new representation of isometric transformations on the group of \(2\)-adic integers, then establish an appropriate ergodicity test. Cited in 2 Documents MSC: 37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps 37A44 Relations between ergodic theory and number theory 37A05 Dynamical aspects of measure-preserving transformations 11E95 \(p\)-adic theory Keywords:\(2\)-adic integers; ergodic transformations × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Anashin, V. S., Uniformly distributed sequences of \(p\)-adic integers, Math. Notes, 55, 1-2, 109-133 (1994) · Zbl 0835.11031 · doi:10.1007/BF02113290 [2] Anashin, V.; Khrennikov, A., Applied Algebraic Dynamics (2009), Berlin: de Gruyter, Berlin · Zbl 1184.37002 [3] Anashin, V.; Khrennikov, A.; Yurova, E., Characterization of ergodicity of \(p\)-adic dynamical systems by using the van der Put basis, Dokl. Math., 83, 3, 1-3 (2011) · Zbl 1247.37007 · doi:10.1134/S1064562411030100 [4] Anashin, V.; Khrennikov, A.; Yurova, E., T-functions revisited: new criteria for bijectivity/transitivity, Des. Codes Cryptog., 71, 3, 383-407 (2014) · Zbl 1338.94059 · doi:10.1007/s10623-012-9741-z [5] Diao, H.; Silva, C. E., Digraph representations of rational functions over the \(p\)-adic numbers, \(p\)-Adic Num. Ultrametr. Anal. Appl., 3, 1, 23-38 (2011) · Zbl 1259.37065 · doi:10.1134/S2070046611010031 [6] Durand, F.; Paccaut, F., Minimal polynomial dynamics on the set of \(3\)-adic integers, Bull. Lond. Math. Soc., 41, 2, 302-314 (2009) · Zbl 1175.37048 · doi:10.1112/blms/bdp003 [7] Fan, A. H.; Li, M. T.; Yao, J. Y.; Zhou, D., Strict ergodicity of affine \(p\)-adic dynamical systems on \(\mathbb{Z}_p \), Adv. Math., 214, 2, 666-700 (2007) · Zbl 1121.37010 · doi:10.1016/j.aim.2007.03.003 [8] Gát, G., On the Fejér kernel functions with respect to the character system of the group of \(2\)-adic integers, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput., 40, 257-267 (2013) · Zbl 1289.42082 [9] Jeong, S., Toward the ergodicity of \(p\)-adic 1-Lipschitz functions represented by the van der Put series, J. Num. Theory, 133, 9, 2874-2891 (2013) · Zbl 1295.37023 · doi:10.1016/j.jnt.2013.02.006 [10] E. Yurova, “Van der Put basis and \(p\)-adic dynamics,” \(p\)-Adic Num. Ultrametr. Anal. Appl. 2 (2), 175-178 (2010). · Zbl 1250.37037 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.