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Multidimensional continued fractions and a Minkowski function

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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 Mönkemeyer continued fraction algorithm with an appropriate tent map.

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Authors and Affiliations

  1. University of Udine, Udine, Italy

    Giovanni Panti

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  1. Giovanni Panti
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Author’s address: Department of Mathematics, University of Udine, via delle Scienze 208, 33100 Udine, Italy

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Panti, G. Multidimensional continued fractions and a Minkowski function. Monatsh Math 154, 247–264 (2008). https://doi.org/10.1007/s00605-008-0535-3

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  • DOI: https://doi.org/10.1007/s00605-008-0535-3

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