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.