Resumen de E-shift radix systems and radix representations with shifted digit sets

Paul Surer

• Let " 2 [0; 1), r 2 Rd and de¯ne the mapping ¿r;" : Zd ! Zd by ¿r;" (z) = (z1; : : : ; zd¡1; ¡brz + "c) (z = (z0; : : : ; zd¡1)) :

  If for each z 2 Zd there is a k 2 N such that the k-th iterate of ¿r;" satis¯es ¿ k r;"(z) = 0 we call ¿r;" an "-shift radix system. In the present paper we unify classical shift radix systems (" = 0) and symmetric shift radix systems (" = 1 2 ), which have already been studied in several papers and analyse the relation of "-shift radix systems to ¯-expansions and canonical number systems with shifted digit sets. At the end we will state several characterisation results for the two dimensional case.