The three-dimensional Gauss algorithm is strongly convergent almost everywhere

D M Hardcastle

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A proof that the three-dimensional Gauss algorithm is strongly convergent almost everywhere is given. This algorithm is equivalent to Brun's algorithm and to the modified Jacobi-Perron algorithm considered by Podsypanin and Schweiger. The proof involves the rigorous computer assisted estimation of the largest Lyapunov exponent of a cocycle associated to the algorithm. To the best of my knowledge, this is the first proof of almost everywhere strong convergence of a Jacobi-Perron type algorithm in dimension greater than two.

Original languageEnglish
Pages (from-to)131-141
Number of pages11
JournalExperimental Mathematics
Volume11
Issue number1
Publication statusPublished - 2002

Keywords

  • Brun's algorithm
  • Jacobi-Perron algorithm
  • Lyapunov exponents
  • Multidimensional continued fractions
  • Strong convergence

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