caa a22 4500 469068574 CHVBK 20180323132915.0 cr unu---uuuuu 170328e19921001xx s 000 0 eng 10.1007/BF02808071 doi (NATIONALLICENCE)springer-10.1007/BF02808071 Generic sequences, transducers and multiplication of normal numbers [Elektronische Daten] [F. Blanchard, J. Dumont, A. Thomas] Existence of a topological joining between two subshiftsX andX′ defines a relation between points of the two. Supposex ∈X is generic for an invariant measureμ onX; when is a relatedx′ ∈X′ also generic for some corresponding measureμ′ onX′? We prove this property holds in several situations for bounded-to-one joinings: whenμ andμ′ are the measures with maximal entropy on intrinsically ergodicX andX′, and also whenμ has a unique preimage on the joining, a property for which several sufficient conditions are given. In the latter case it is also possible to prove that the nearer a point is to genericity with respect toμ, the nearer to genericity with respect toμ′ a related point is. Bounded-to-one joinings may be defined by nonambiguous rational transductions. This provides several applications, most of them in Number Theory. It is proven that transducers performing multiplication by integers have the suitable properties: this implies multiplication by a rational preserves near normality; so does addition of a rational. An application to Markov measures, and sufficient conditions for a transducer to map normality to the basep to normality to the basep′, p′≠p, are given. Hebrew University, 1992 Blanchard F. Laboratoire de Mathématiques Discrètes, Case 930, 163 av. de Luminy, 13288, Marseille Cedex 9, France aut Dumont J. Département de Math-Info, Faculté des Sciences de Luminy, 163 av. de Luminy, 13288, Marseille Cedex 9, France aut Thomas A. Université de Provence, Case F, 3 place Victor Hugo, 13331, Marseille Cedex 3, France aut Israel Journal of Mathematics Springer-Verlag 80/3(1992-10-01), 257-287 0021-2172 80:3<257 1992 80 11856 https://doi.org/10.1007/BF02808071 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02808071 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Blanchard F. Laboratoire de Mathématiques Discrètes, Case 930, 163 av. de Luminy, 13288, Marseille Cedex 9, France aut NATIONALLICENCE 700 1- Dumont J. Département de Math-Info, Faculté des Sciences de Luminy, 163 av. de Luminy, 13288, Marseille Cedex 9, France aut NATIONALLICENCE 700 1- Thomas A. Université de Provence, Case F, 3 place Victor Hugo, 13331, Marseille Cedex 3, France aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 80/3(1992-10-01), 257-287 0021-2172 80:3<257 1992 80 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer