Topological conjugation classes of tightly transitive subgroups of Homeo₊(ℝ)

Enhui Shi, and Lizhen Zhou. "Topological conjugation classes of tightly transitive subgroups of Homeo₊(ℝ)." Colloquium Mathematicae 145.1 (2016): 111-120. <http://eudml.org/doc/286392>.

@article{EnhuiShi2016,
abstract = {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.},
author = {Enhui Shi, Lizhen Zhou},
journal = {Colloquium Mathematicae},
keywords = {topological transitivity; homeomorphism group; topological conjugation},
language = {eng},
number = {1},
pages = {111-120},
title = {Topological conjugation classes of tightly transitive subgroups of Homeo₊(ℝ)},
url = {http://eudml.org/doc/286392},
volume = {145},
year = {2016},
}

TY - JOUR
AU - Enhui Shi
AU - Lizhen Zhou
TI - Topological conjugation classes of tightly transitive subgroups of Homeo₊(ℝ)
JO - Colloquium Mathematicae
PY - 2016
VL - 145
IS - 1
SP - 111
EP - 120
AB - 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.
LA - eng
KW - topological transitivity; homeomorphism group; topological conjugation
UR - http://eudml.org/doc/286392
ER -