10 citations · 13 across the 12 of their papers we have counts for
12 papers
Brjuno condition through best approximations and the linearization problem
Nicolas Chevallier, João Lopes Dias, José Pedro Gaivão +2
We consider the classical analytic linearization problem for vector fields on the torus close to a constant vector field . Our goals are twofold. First, we provid…
Ergodicity of cocyles over 2-dimensional rotations
Nicolas Chevallier, Jean-Pierre Conze
We study recurrence and ergodicity of cocycles with values in R d , d 1, over rotations by badly approximable irrational numbers on T , \> 1. The discontinuities o…
A dynamical view of Tijdeman's solution of the chairman assignment problem
Valérie Berthé, Olivier Carton, Nicolas Chevallier +2
In 1980, R. Tijdeman provided an on-line algorithm that generates sequences over a finite alphabet with minimal discrepancy, that is, such that the occurrence of each letter optima…
About the value of the two dimensional Levy's constant
Yitwah Cheung, Nicolas Chevallier
We give a numerical approximation of the Lévy constant on the growth of the denominators of the best Diophantine approximations in dimension 2 with respect to the euclidean norm. T…
The natural extension of the Gauss map and Hermite best approximations
Nicolas Chevallier
Hermite best approximation vectors of a real number were introduced by Lagarias. A nonzero vector (p, q) Z x N is a Hermite best approximation vector of if there exis…
Gauss lattices and complex continued fractions
Nicolas Chevallier
Our aim is to find a complex continued fraction algorithm finding all the best Diophantine approximations to a complex number. Using the sequence of minimal vectors in a two dimens…
Dynamic of generalized transvections
Guido Ahumada, Nicolas Chevallier
Given an increasing odd homeomorphism : R R, the two bijective maps h , v : R 2 R 2 dened by h (x, y) = (x + --1 (y), y) and v (…
Levy-Khintchin Theorem for best simultaneous Diophantine approximations
Yitwah Cheung, Nicolas Chevallier
We extend two results about the ordinary continued fraction expansion to best simultaneous Diophantine approximations of vectors or matrices. The first is Levy-Khintchin Theorem ab…
Fixating Group Actions
Guido Ahumada, Bernard Brighi, Nicolas Chevallier +1
A group of bijections G acting on a set X is said with fixed points (abbreviated as gaf from the french "groupe {à} points fixes") if any element of G has at least one fixed point…
Hausdorff dimension and uniform exponents in dimension two
Yann Bugeaud, Yitwah Cheung, Nicolas Chevallier
In this paper we prove the Hausdorff dimension of the set of (nondegenerate) singular two-dimensional vectors with uniform exponent (1/2, 1) is 2(1 -- ) when …
What is the minimal cardinal of a family which shatters all d-subsets of a finite set?
N. Chevallier, A. Fruchard
What is the minimal cardinal of a family which shatters all d-subsets of a finite set?
Envelopes of -sections
Nicolas Chevallier, Augustin Fruchard, Costin Vîlcu
Let be a planar convex body af area , and take $0 \textless{} α\textless{} 1$.An -section of is a line cutting into two parts, one of whichhas area . This…