Some Dynamic Properties of the Modified Negative Slope Algorithm

Abstract

S. Ferenczi and L. F. C. da Rocha introduced an algorithm which is slightly different form of the negative slope algorithm as the normalized multiplicative algorithm deduced from three interval exchange transformations. It has the form that the ceiling value is taken in the case of \( x+y > 1 \). We call this algorithm as the ``modified negative slope algorithm''. In this paper, the author shows that the modified negative slope algorithm is weak Bernoulli with respect to the absolutely continuous invariant measure and gives an algebraic characterization of periodic orbits of this algorithm using the natural extension method.