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arXiv · 0705.0584

Multidimensional continued fractions and a Minkowski function

Giovanni Panti
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Abstract

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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Giovanni Panti. 2007-10-02. Multidimensional continued fractions and a Minkowski function. https://arxiv.org/abs/0705.0584

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