Multidimensional continued fractions and a Minkowski function

Details Multidimensional continued fractions and a Minkowski function Multidimensional continued fractions and a Minkowski function

2007-05-04

arxiv.org/abs/0705.0584v2

Mathematics

Number Theory

17 pages, 3 figures. Revised version according to the referee's suggestions. Proof of Lemma 2.3 more detailed, other minor mod

Scientific paper

The Minkowski Question Mark function can be characterized as the unique homeomorphism of the real unit interval that conjugates the Farey map with the tent map. We construct an n-dimensional analogue of the Minkowski function as the only homeomorphism of an n-simplex that conjugates the piecewise-fractional map associated to the Monkemeyer continued fraction algorithm with an appropriate tent map.

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