Abstract

Using the numeration system associated to the substitution 1 --> 12, 2 --> 31, 3 --> 1, we define a binary operation, which generates a semigroup on a subset of N. This semigroup represents the self-similar structure defined by an Iterated Function System (IFS) on the dynamical system associated to this substitution. (C) 1998 Elsevier Science Ltd. All rights reserved.