Dynamical analysis of α-Euclidean algorithms

We study a class of Euclidean algorithms related to divisions where the remainder is constrained to belong to [ α−1, α], for some α∈[0,1]. The paper is devoted to the average-case analysis of these algorithms, in terms of number of steps or bit-complexity. This is a new instance of the so-called “dynamical analysis” method, where dynamical systems are made a deep use of. Here, the dynamical systems of interest have an infinite number of branches and they are not Markovian, so that the general framework of dynamical analysis is more complex to adapt to this case than previously.