Entropy of the induced transformations associated with the interval algorithm

抄録

We have introduced the induced transformations associated with the interval algorithm. In view of the entropy of the induced transformations, the stopping time of the algorithm is evaluated. Sharp upper and lower bounds on the mean value of the stopping time are given for the case that the source and the target have uniform distributions. We generalize these bounds to the case that the source and the target have arbitrary distributions whose elements are all rational numbers.