%0 Journal Article
%T Cross sections for geodesic flows and \alpha-continued fractions
%+ Institut de mathématiques de Luminy (IML)
%+ Oregon State University (OSU)
%A Arnoux, Pierre
%A Schmidt, Thomas A.
%Z 20 pages, 2 figures
%< avec comité de lecture
%@ 0951-7715
%J Nonlinearity
%I IOP Publishing
%V 26
%N 3
%8 2013-03
%D 2013
%Z 1207.7299
%R 10.1088/0951-7715/26/3/711
%Z Mathematics [math]/Dynamical Systems [math.DS]
%Z Mathematics [math]/Number Theory [math.NT]Journal articles
%X 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 the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.
%G English
%L hal-01265582
%U https://hal.science/hal-01265582
%~ CNRS
%~ UNIV-AMU
%~ IML
%~ I2M
%~ TDS-MACS