English

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

R2 v1 2026-06-21T17:45:52.944Z