Denominator-preserving maps
Number Theory
2011-05-10 v2 Dynamical Systems
Abstract
Let F be a continuous injective map from an open subset of R^n 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.
Keywords
Cite
@article{arxiv.1103.5473,
title = {Denominator-preserving maps},
author = {Giovanni Panti},
journal= {arXiv preprint arXiv:1103.5473},
year = {2011}
}
Comments
11 pages, 1 figure