English

Times two, three, five orbits on $\mathbb{T}^2$

Dynamical Systems 2022-02-14 v2 Number Theory

Abstract

In this paper, we study orbit closures under diagonal torus actions. We show that if (x,y)T2(x,y)\in\mathbb{T}^2 is not contained in any rational lines, then its orbit under the ×2,×3,×5\times 2, \times 3, \times 5 actions is dense in T2.\mathbb{T}^2.

Cite

@article{arxiv.2009.00441,
  title  = {Times two, three, five orbits on $\mathbb{T}^2$},
  author = {Han Yu},
  journal= {arXiv preprint arXiv:2009.00441},
  year   = {2022}
}

Comments

14 pages, 1 figure; Version accepted in Adv. Math

R2 v1 2026-06-23T18:14:21.442Z