The purpose of this paper is to describe the relation between the Leg-endre and the Lenstra constants. Indeed we show that they are equal whenever the Legendre constant exists; in particular, this holds for both Rosen continued fractions and α-continued fractions. We also give the explicit value of the entropy of the Rosen map with respect to the absolutely… (More)
We consider metric results for the asymptotic behavior of the number of solutions of Diophantine approximation inequalities with restricted denominators for Lau-rent formal power series with coefficients in a finite field. We especially consider approximations by rational functions whose denominators are powers of irreducible polynomials, and study the… (More)
Let Ω be a Borel subset of S N where S is countable. A measure is called exchangeable on Ω, if it is supported on Ω and is invariant under every Borel automorphism of Ω which permutes at most finitely many coordinates. De-Finetti's theorem characterizes these measures when Ω = S N. We apply the ergodic theory of equivalence relations to study the case Ω = S… (More)
In a recent paper, the first and third author proved a central limit theorem for the number of coprime solutions of the diophantine approximation problem for formal Laurent series in the setting of the classical theorem of Khintchine. In this note, we consider a more general setting and show that even an invariance principle holds, thereby improving upon… (More)
We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of " symmetric measure " : exchangeability and the Gibbs property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one dimensional case) exhibit a variety of spectral properties.
We investigate the mixing coefficients of interval maps satisfying Rych-lik's conditions. A mixing Lasota-Yorke map is reverse φ-mixing. If its invariant density is uniformly bounded away from 0, it is φ-mixing iff all images of all orders are big in which case it is ψ-mixing. Among β-transformations, non-φ-mixing is generic. In this sense, the asymmetry of… (More)
This paper studies digit-cost functions for the Euclid algorithm on polynomials with coefficients in a finite field, in terms of the number of operations performed on the finite field Fq. The usual bit-complexity is defined with respect to the degree of the quotients; we focus here on a notion of 'fine' complexity (and on associated costs) which relies on… (More)