Continued fractions and the d-dimensional Gauss transformation

D. M. Hardcastle, K. Khanin

Research output: Contribution to journalArticle

Abstract

In this paper we study a multidimensional continued fraction algorithm which is related to the Modified Jacobi-Perron algorithm considered by Podsypanin and Schweiger. We demonstrate that this algorithm has many important properties which are natural generalisations of properties of one-dimensional continued fractions. For this reason, we call the transformation associated to the algorithm the d-dimensional Gauss transformation. We construct a coordinate system for the natural extension which reveals its symmetries and allows one to give an explicit formula for the density of its invariant measure. We also discuss the ergodic properties of this invariant measure.

Original languageEnglish
Pages (from-to)487-515
Number of pages29
JournalCommunications in Mathematical Physics
Volume215
Issue number3
DOIs
Publication statusPublished - Jan 2001

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Continued fraction
Gauss
Invariant Measure
Natural Extension
Jacobi
Explicit Formula
Symmetry
Demonstrate

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Hardcastle, D. M. ; Khanin, K. / Continued fractions and the d-dimensional Gauss transformation. In: Communications in Mathematical Physics. 2001 ; Vol. 215, No. 3. pp. 487-515.
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Continued fractions and the d-dimensional Gauss transformation. / Hardcastle, D. M.; Khanin, K.

In: Communications in Mathematical Physics, Vol. 215, No. 3, 01.2001, p. 487-515.

Research output: Contribution to journalArticle

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