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2002 The Three-Dimensional Gauss Algorithm is Strongly Convergent Almost Everywhere
D. M. Hardcastle
Experiment. Math. 11(1): 131-141 (2002).

Abstract

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.

Citation

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D. M. Hardcastle. "The Three-Dimensional Gauss Algorithm is Strongly Convergent Almost Everywhere." Experiment. Math. 11 (1) 131 - 141, 2002.

Information

Published: 2002
First available in Project Euclid: 10 July 2003

zbMATH: 1022.11034
MathSciNet: MR1960307

Subjects:
Primary: 11J70
Secondary: 11K50

Rights: Copyright © 2002 A K Peters, Ltd.

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Vol.11 • No. 1 • 2002
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