Let ℝ be the real line and let Homeo₊(ℝ) be the orientation preserving homeomorphism group of ℝ. Then a subgroup G of Homeo₊(ℝ) is called tightly transitive if there is some point x ∈ X such that the orbit Gx is dense in X and no subgroups H of G with |G:H| = ∞ have this property. In this paper, for each integer n > 1, we determine all the topological conjugation classes of tightly transitive subgroups G of Homeo₊(ℝ) which are isomorphic to ℤⁿ and have countably many nontransitive points.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6627-1-2016,
author = {Enhui Shi and Lizhen Zhou},
title = {Topological conjugation classes of tightly transitive subgroups of Homeo+(R)},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {111-120},
zbl = {06602774},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6627-1-2016}
}
Enhui Shi; Lizhen Zhou. Topological conjugation classes of tightly transitive subgroups of Homeo₊(ℝ). Colloquium Mathematicae, Tome 144 (2016) pp. 111-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6627-1-2016/