Characterization of periodic points of the negative slope algorithm

Abstract

The notion of negative slope algorithm was introduced by S. Ferenczi, C. Holton, and L. Zamboni in their study of the three letter languages arising from three interval exchange transformations. They characterize eventually periodic points of the negative slope algorithm. In this paper, by using the natural extension of the negative slope algorithm, we give a necessary and sufficient condition for purely periodicity of the negative slope algorithm.