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On Almost Everywhere Strong Convergence of Multidimensional Continued Fraction Algorithms
Hardcastle, D.M.; Khanin, K.
HPL-BRIMS-2000-12
Keyword(s): simultaneous diophantine approximations; Jacobi-Perron algorithm; multidimensional continued fractions; strong convergence; Lyapunov exponents
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. Notes: D.M. Hardcastle, Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, U.K.
25 Pages
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