24 citations · 56 across the 9 of their papers we have counts for
7 papers · 1 filter
Arnoux-Rauzy interval exchange transformations
Pierre Arnoux, Julien Cassaigne, Sébastien Ferenczi +1
The Arnoux-Rauzy systems are defined in \cite{ar}, both as symbolic systems on three letters and exchanges of six intervals on the circle. In connection with a conjecture of S.P. N…
Natural extensions and Gauss measures for piecewise homographic continued fractions
Pierre Arnoux, Thomas A. Schmidt
We give a heuristic method to solve explicitly for an absolutely continuous invariant measure for a piecewise differentiable, expanding map of a compact subset of Euclidean spa…
On some symmetric multidimensional continued fraction algorithms
Pierre Arnoux, Sébastien Labbé
We compute explicitly the density of the invariant measure for the Reverse algorithm which is absolutely continuous with respect to Lebesgue measure, using a method proposed by Arn…
Commensurable continued fractions
Pierre Arnoux, Thomas A. Schmidt
We compare two families of continued fractions algorithms, the symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms expands real numbers in terms of certai…
Random product of substitutions with the same incidence matrix
Pierre Arnoux, Masahiro Mizutani, Tarek Sellami
Any infinite sequence of substitutions with the same matrix of the Pisot type defines a symbolic dynamical system which is minimal. We prove that, to any such sequence, we can asso…
Cross sections for geodesic flows and α-continued fractions
Pierre Arnoux, Thomas A. Schmidt
We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of…