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On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof

Published online by Cambridge University Press:  14 October 2010

T. Fujita ,
S. Ito ,
M. Keane  and
M. Ohtsuki
T. Fujita
Affiliation:
Department of Mathematics, Hitotubashi University, Kunitachi, Tokyo, Japan, (e-mail: fujita@math.hit-u.ac.jp)
S. Ito
Affiliation:
Department of Mathematics, Tsuda College, Tsuda-machi, Kodaira, Tokyo, Japan, (e-mail: ito@tsuda.ac.jp) (e-mail: ohtsuki@tsuda.ac.jp)
M. Keane
Affiliation:
Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands, (e-mail: keane@cwi.nl)
M. Ohtsuki
Affiliation:
Department of Mathematics, Tsuda College, Tsuda-machi, Kodaira, Tokyo, Japan, (e-mail: ito@tsuda.ac.jp) (e-mail: ohtsuki@tsuda.ac.jp)
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The following theorem was published in [2].

Theorem. There exists a constant δ > 0 such that for Lebesgue almost every (α, β) ∈ X = [0, 1] × [0, 1], there exists no = no(α, β) such that for any n > no

where the integers pn, qn, rn are provided by the modified Jacobi-Perron algorithm.

Type
Corrigendum
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 6 , December 1996 , pp. 1345 - 1352
Copyright
Copyright © Cambridge University Press 1996

References

REFERENCES

[1] Gantmacher, F. R.. The Theory of Matrices (2 vols). Chelsea, New York, 1964.Google Scholar
[2] Ito, S., Keane, M. and Ohtsuki, M.. Almost everywhere exponential convergence of the modified Jacobi-Perron algorithm. Ergod. Th. & Dynam. Sys. 13 (1993), 319–334.CrossRefGoogle Scholar