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.
Publié le : 2002-05-14
Classification:
Multidimensional continued fractions,
Brun's algorithm,
Jacobi-Perron algorithm,
strong convergence,
Lyapunov exponents,
11J70,
11K50
@article{1057860320,
author = {Hardcastle, D. M. and Khanin, K.},
title = {The d-Dimensional Gauss Transformation: Strong Convergence and Lyapunov Exponents},
journal = {Experiment. Math.},
volume = {11},
number = {3},
year = {2002},
pages = { 119-129},
language = {en},
url = {http://dml.mathdoc.fr/item/1057860320}
}
Hardcastle, D. M.; Khanin, K. The d-Dimensional Gauss Transformation: Strong Convergence and Lyapunov Exponents. Experiment. Math., Tome 11 (2002) no. 3, pp. 119-129. http://gdmltest.u-ga.fr/item/1057860320/