A two-dimensional continued fractions algorithm with Lagrange and Dirichlet properties

Abstract

A Lagrange Theorem in dimension 2 is proved, for a particular two-dimensional algorithm, with a very natural geometrical definition. Dirichlet-type properties for the convergence of the algorithm are also proved. These properties procced from a geometrical quality of the algorithm. Some refercences are given to the works of various authors, in the domain of multidimensional continued fractions algorithms.

arXiv commentPublished in the Journal de Théorie des Nombres de Bordeaux