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

Hardcastle, D.M. ; Khanin, K.

HPL-BRIMS-2000-26

Keyword(s): multi-dimensional continued fractions; computer assisted proof

Abstract: 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 modified Jacobi-Perron algorithm considered by Podsypanin and Schweiger. In this paper we focus on the reduction of the problem to a finite 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. Notes: D.M. Hardcastle, Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, UK

18 Pages

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