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On almost everywhere strong convergence of multi-dimensional continued fraction algorithms

Published online by Cambridge University Press:  01 December 2000

D. M. HARDCASTLE  and
K. KHANIN
D. M. HARDCASTLE
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK (e-mail: D.M.Hardcastle@ma.hw.ac.uk)
K. KHANIN
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK (e-mail: D.M.Hardcastle@ma.hw.ac.uk) Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, UK BRIMS, Hewlett-Packard Laboratories, Stoke Gifford, Bristol BS126QZ, UK Landau Institute for Theoretical Physics, Kosygina Str., 2, Moscow 117332, Russia
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Abstract

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We describe a strategy which allows one to produce computer assisted proofs of almost everywhere strong convergence of Jacobi–Perron type algorithms in arbitrary dimension. Numerical work is carried out in dimension three to illustrate our method. To the best of our knowledge this is the first result on almost everywhere strong convergence in dimension greater than two.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 6 , December 2000 , pp. 1711 - 1733
Copyright
© 2000 Cambridge University Press