The d-Dimensional Gauss Transformation: Strong Convergence and Lyapunov Exponents

We discuss a method of producing computer assisted proofs of almost everywhere strong convergence of the d-dimensional Gauss algorithm. This algorithm is equivalent to Brun's algorithm and to the modi ed Jacobi-Perron algorithm considered by Podsypanin and Schweiger. In this paper we focus on the reduction of the problem to a nite number of calculations. These calculations have been carried out for the three-dimensional algorithm and the results, which prove almost everywhere strong convergence, will be published separately.