The Three-Dimensional Gauss Algorithm Is Strongly Convergent Almost Everywhere

DOI10.1080/10586458.2002.10504475zbMath1022.11034OpenAlexW2082996901MaRDI QIDQ4804811

D. M. Hardcastle

Publication date: 26 October 2003

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1057860321

zbMATH Keywords

strong convergenceLyapunov exponentsJacobi-Perron algorithmBrun's algorithmmultidimensional continued fractions

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Metric theory of continued fractions (11K50)

Related Items (6)

Multidimensional continued fractions, dynamical renormalization and KAM theory ⋮ Multidimensional continued fractions and symbolic codings of toral translations ⋮ What do continued fractions accomplish? ⋮ On the second Lyapunov exponent of some multidimensional continued fraction algorithms ⋮ Zero measure spectrum for multi-frequency Schrödinger operators ⋮ Almost everywhere balanced sequences of complexity \(2n + 1\)

Cites Work

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• The quality of the diophantine approximations found by the Jacobi--Perron algorithm and related algorithms
• A multidimensional continued fraction and some of its statistical properties
• A convergence exponent for multidimensional continued-fraction algorithms
• A simple proof of the exponential convergence of the modified Jacobi–Perron algorithm
• On almost everywhere strong convergence of multi-dimensional continued fraction algorithms
• Thed-Dimensional Gauss Transformation: Strong Convergence and Lyapunov Exponents
• On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof
• Continued fractions and the \(d\)-dimensional Gauss transformation

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