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Denominator-preserving maps

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Abstract

Let F be a continuous injective map from an open subset of \({\mathbb {R}^n}\) to \({\mathbb {R}^n}\) . Assume that, for infinitely many k ≥ 1, F induces a bijection between the rational points of denominator k in the domain and those in the image (the denominator of (a 1/b 1, . . . , a n /b n ) being the l.c.m. of b 1, . . . , b n ). Then F preserves the Lebesgue measure.

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  1. Department of Mathematics, University of Udine, via delle Scienze 208, 33100, Udine, Italy

    Giovanni Panti

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  1. Giovanni Panti
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Correspondence to Giovanni Panti.

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Panti, G. Denominator-preserving maps. Aequat. Math. 84, 13–25 (2012). https://doi.org/10.1007/s00010-011-0102-1

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