A multidimensional continued fraction and some of its statistical properties

DOI10.1007/BF01054430zbMath0891.11039OpenAlexW1996121512MaRDI QIDQ1203279

P. R. Baldwin

Publication date: 1 September 1994

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01054430

zbMATH Keywords

Kolmogorov-Sinai entropygeneralized mediant algorithmapproximating irrational numbersmultidimensional continued-fraction algorithm

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Entropy and other invariants (28D20) Ergodic theory (37A99) Metric theory of continued fractions (11K50) Approximation by numbers from a fixed field (11J17)

Related Items (7)

The Three-Dimensional Gauss Algorithm Is Strongly Convergent Almost Everywhere ⋮ On the second Lyapunov exponent of some multidimensional continued fraction algorithms ⋮ Multidimensional continued fractions and a Minkowski function ⋮ The quality of the diophantine approximations found by the Jacobi--Perron algorithm and related algorithms ⋮ 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) ⋮ A multidimensional continued fraction based on a high-order recurrence relation ⋮ Almost everywhere exponential convergence of the modified Jacobi—Perron algorithm

Cites Work

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• Diophantine approximation
• A convergence exponent for multidimensional continued-fraction algorithms
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• The metrical theory of Jacobi-Perron algorithm
• Presentation functions, fixed points, and a theory of scaling function dynamics.
• A mean-field approximation for the maximum Lyapunov exponent of Bernoulli trials of matrices
• Applications of Number Theory to Numerical Analysis
• Geodesic Multidimensional Continued Fractions
• Ergodic theory of chaos and strange attractors
• Some ergodic properties of multi-dimensional f-expansions

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