2013/09/03 by Pierre Arnoux, Thomas A. Schmidt, Thomas Schmidt +2
Mathematics · Physics and Astronomy · #11K50 #30B70 #37D40 #37E05 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Waves and Solitons #math.DS #msc:11K50 #msc:30B70 #msc:37D40 #msc:37E05
paper · pdf · doi:10.48550/arxiv.1309.0760
41 pages, 10 figures
arxiv created 2013/09/03 · openalex publication_date 2013/09/03 · arxiv updated 2013/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 certain algebraic integers. We give explicit models of the natural extension of the maps associated with these algorithms; prove that these natural extensions are in fact conjugate to the first return map of the geodesic flow on a related surface; and, deduce that, up to a conjugacy, almost every real number has an infinite number of common approximants for both algorithms.