The d-dimensional gauss transformation: Strong convergence and lyapunov exponents

D. M. Hardcastle, K. Khanin

Research output: Contribution to journalLiterature reviewpeer-review


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
JournalHP Laboratories Technical Report
Issue number26
Publication statusPublished - 18 Dec 2000


  • Computer assisted proof
  • Multi-dimensional continued fractions


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