Denominatorpreserving maps
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.
 Publication:

arXiv eprints
 Pub Date:
 March 2011
 arXiv:
 arXiv:1103.5473
 Bibcode:
 2011arXiv1103.5473P
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Dynamical Systems;
 28D05;
 11K06
 EPrint:
 11 pages, 1 figure