Intrinsic ergodicity of affine maps in [0, 1](d)

We consider the discontinuous dynamical systems on [0,1](d) defined by expanding affine maps considered module Z(d). We study their invariant probability measures which maximize entropy. We show that they form a non-empty, finite-dimensional simplex and reduce the question of their multiplicity to a topological problem. We also give a description of these measures. These results are obtained by using a generalization of F. Hofbauer's Markov Diagram previously developed by the author for the study of non-piecewise monotonic, smooth interval maps. This paper is intended as a simple but non-trivial application of this technique in higher dimension.