5 papers
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 (…
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…