The d-dimensional Gauss transformation: Strong convergence and Lyapunov exponents

D. M. Hardcastle, K. Khanin

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We discuss a method of producing computer assisted proofs of almost everywhere strong convergence of the d-dimensional Gauss algorithm. This algorithm is equivalent to Brun's algorithm and to the modified Jacobi-Perron algorithm considered by Podsypanin and Schweiger. In this paper we focus on the reduction of the problem to a finite number of calculations. These calculations have been carried out for the three-dimensional algorithm and the results, which prove almost everywhere strong convergence, will be published separately.

Original languageEnglish
Pages (from-to)119-129
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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