Denominator-preserving maps

Published 28 Mar 2011 in math.NT and math.DS | (1103.5473v2)

Abstract: Let F be a continuous injective map from an open subset of Rⁿ to 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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Giovanni Panti

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