The three-dimensional Gauss algorithm is strongly convergent almost everywhere.
Hardcastle, D.M. (2002)
Experimental Mathematics
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Displaying similar documents to “The -dimensional Gauss transformation: Strong convergence and Lyapunov exponents.”
The three-dimensional Gauss algorithm is strongly convergent almost everywhere.
On the invariant measure for Jacobi-Perron algorithm.
Schweiger, F. (1990)
Mathematica Pannonica
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The Jacobi-Perron Algorithm and Pisot numbers
Eugène Dubois, Ahmed Farhane, Roger Paysant-Le Roux (2004)
Acta Arithmetica
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Volume as a measure of approximation for the Jacobi-Perron algorithm.
Schweiger, Fritz (2010)
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A Note on a One-sided Jacobi Algorithm.
K. Veselic, V. Hari (1989/90)
Numerische Mathematik
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A Jacobi eigenreduction algorithm for definite matrix pairs.
K. Veselic (1993)
Numerische Mathematik
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The Number of Steps in a Finite Jacobi Algorithm.
Roland Fischer, Fritz Schweiger (1975)
Manuscripta mathematica
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Ergodic Computations with Continued Fractions and Jacobi's Algorithm.
M.S. Waterman, W.A. Beyer (1972)
Numerische Mathematik
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Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems
Brigitte Vallée (2000)
Journal de théorie des nombres de Bordeaux
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We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory...
Discrete planes, -actions, Jacobi-Perron algorithm and substitutions
Pierre Arnoux, Valérie Berthé, Shunji Ito (2002)
Annales de l’institut Fourier
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We introduce two-dimensional substitutions generating two-dimensional sequences related to discrete approximations of irrational planes. These two-dimensional substitutions are produced by the classical Jacobi-Perron continued fraction algorithm, by the way of induction of a -action by rotations on the circle. This gives a new geometric interpretation of the Jacobi-Perron algorithm, as a map operating on the parameter space of -actions by rotations.
Periodic multiplicative algorithms of Selmer type.
Schweiger, Fritz (2005)
Integers
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