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

• Autorzy: Enhui Shi , Lizhen Zhou
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57S25: Groups acting on specific manifolds
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 145
• Numer: 1
• Strony: 111-120

Daty

wydano

2016

Twórcy

autor

Enhui Shi

• School of Mathematical Sciences, Soochow University, Suzhou 215006, P.R. China

autor

Lizhen Zhou

• School of Mathematical Sciences, Soochow University, Suzhou 215006, P.R. China

Identyfikatory

DOI

10.4064/cm6627-1-2016