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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
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK (e-mail: [email protected])
K. KHANIN
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK (e-mail: [email protected]) 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

Abstract

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
Copyright
© 2000 Cambridge University Press

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