Displaying similar documents to “A two-dimensional continued fraction algorithm for best approximations with an application in cubic number fields.”

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

Christian Drouin (2014)

Journal de Théorie des Nombres de Bordeaux

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A Lagrange Theorem in dimension 2 is proved in this paper, for a particular two dimensional continued fraction algorithm, with a very natural geometrical definition. Dirichlet type properties for the convergence of this algorithm are also proved. These properties proceed from a geometrical quality of the algorithm. The links between all these properties are studied. In relation with this algorithm, some references are given to the works of various authors, in the domain of multidimensional...