Thed-Dimensional Gauss Transformation: Strong Convergence and Lyapunov Exponents

DOI10.1080/10586458.2002.10504474zbMath1029.11037OpenAlexW2115906782MaRDI QIDQ4804810

D. M. Hardcastle, Konstantin M. Khanin

Publication date: 5 February 2004

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

Full work available at URL: https://eudml.org/doc/50500

zbMATH Keywords

strong convergenceLyapunov exponentsJacobi-Perron algorithmBrun's algorithmGauss transformationMultidimensional continued fractions

Mathematics Subject Classification ID

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

Related Items (6)

The Three-Dimensional Gauss Algorithm Is Strongly Convergent Almost Everywhere ⋮ The Brun gcd algorithm in high dimensions is almost always subtractive ⋮ Multidimensional continued fractions, dynamical renormalization and KAM theory ⋮ What do continued fractions accomplish? ⋮ On the second Lyapunov exponent of some multidimensional continued fraction algorithms ⋮ Almost everywhere balanced sequences of complexity \(2n + 1\)

Cites Work

• The quality of the diophantine approximations found by the Jacobi--Perron algorithm and related 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
• On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof
• Exposants caractéristiques de l'algorithme de Jacobi-Perron et de la transformation associée. (Characteristic exponents of the Jacobi-Perron algorithm and of the associated map)
• Continued fractions and the \(d\)-dimensional Gauss transformation
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