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Continued Fractions and the ddimensional Gauss Transformation
Hardcastle, D.M.; Khanin, K.
HPLBRIMS200015
Keyword(s): multidimensional Gauss transformation; natural extension; invariant measure
Abstract: In this paper we study a multidimensional continued fraction algorithm which is related to the Modified JacobiPerron algorithm considered by Podsypanin and Schweiger. We demonstrate that this algorithm has many important properties which are natural generalisations of properties of onedimensional continued fractions. For this reason, we call the transformation associated to the algorithm the ddimensional 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. Notes: D.M. Hardcastle, Department of Mathematics, HeriotWatt University, Edinburgh, EH14 4AS, UK.
31 Pages
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