The Three-Dimensional Gauss Algorithm is Strongly Convergent Almost Everywhere
Hardcastle, D. M.
Experiment. Math., Tome 11 (2002) no. 3, p. 131-141 / Harvested from Project Euclid
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A proof that the three-dimensional Gauss algorithm is strongly convergent almost everywhere is given. This algorithm is equivalent to Brun's algorithm and to the modified Jacobi-Perron algorithm considered by Podsypanin and Schweiger. The proof involves the rigorous computer assisted estimation of the largest Lyapunov exponent of a cocycle associated to the algorithm. To the best of my knowledge, this is the first proof of almost everywhere strong convergence of a Jacobi-Perron type algorithm in dimension greater than two.
Publié le : 2002-05-14
Classification:  Multidimensional continued fractions,  Brun's algorithm,  Jacobi-Perron algorithm,  strong convergence,  Lyapunov exponents,  11J70,  11K50 
@article{1057860321,
     author = {Hardcastle, D. M.},
     title = {The Three-Dimensional Gauss Algorithm is Strongly Convergent Almost Everywhere},
     journal = {Experiment. Math.},
     volume = {11},
     number = {3},
     year = {2002},
     pages = { 131-141},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1057860321}
}

Hardcastle, D. M. The Three-Dimensional Gauss Algorithm is Strongly Convergent Almost Everywhere. Experiment. Math., Tome 11 (2002) no. 3, pp.  131-141. http://gdmltest.u-ga.fr/item/1057860321/