Continued fractions and Brjuno functions
Proceedings of the conference on Continued fractions and geometric function theory
Analytic Analysis of Algorithms
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Dynamical Analysis of the Parametrized Lehmer–Euclid Algorithm
Combinatorics, Probability and Computing
Existence of a limiting distribution for the binary GCD algorithm
Journal of Discrete Algorithms
Generalized Brjuno functions associated to α-continued fractions
Journal of Approximation Theory
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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.