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

100%

Shi E., Zhou L.

Colloquium Mathematicum

2016

tom 145

nr 1

111-120

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.

Topological transitivity of solvable group actions on the line ℝ

81%

Wang S., Shi E., Zhou L., Cairns G.

Colloquium Mathematicum

2009

tom 116

nr 2

203-215

Let ϕ:G → Homeo₊(ℝ) be an orientation preserving action of a discrete solvable group G on ℝ. In this paper, the topological transitivity of ϕ is investigated. In particular, the relations between the dynamical complexity of G and the algebraic structure of G are considered.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Shi E.

2 Zhou L.

1 Cairns G.

1 Wang S.

1 2016

1 2009

Wyniki wyszukiwania

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

Topological transitivity of solvable group actions on the line ℝ