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2002 The d-Dimensional Gauss Transformation: Strong Convergence and Lyapunov Exponents
D. M. Hardcastle, K. Khanin
Experiment. Math. 11(1): 119-129 (2002).

Abstract

We discuss a method of producing computer assisted proofs of almost everywhere strong convergence of the d-dimensional Gauss algorithm. This algorithm is equivalent to Brun's algorithm and to the modified Jacobi-Perron algorithm considered by Podsypanin and Schweiger. In this paper we focus on the reduction of the problem to a finite number of calculations. These calculations have been carried out for the three-dimensional algorithm and the results, which prove almost everywhere strong convergence, will be published separately.

Citation

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D. M. Hardcastle. K. Khanin. "The d-Dimensional Gauss Transformation: Strong Convergence and Lyapunov Exponents." Experiment. Math. 11 (1) 119 - 129, 2002.

Information

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

zbMATH: 1029.11037
MathSciNet: MR1960306

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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