English

The realization and classification of topologically transitive group actions on $1$-manifolds

Dynamical Systems 2019-10-28 v1

Abstract

In this report, we first recall the Poincar\'e's classification theorem for minimal orientation-preserving homeomorphisms on the circle and the Ghys' classification theorem for minimal orientation-preserving group actions on the circle. Then we introduce a classification theorem for a specified class of topologically transitive orientation-preserving group actions on the circle by Zd\mathbb Z^d. Also, some groups that admit/admit no topologically transitive actions on the line are determined.

Keywords

Cite

@article{arxiv.1910.11728,
  title  = {The realization and classification of topologically transitive group actions on $1$-manifolds},
  author = {Enhui Shi},
  journal= {arXiv preprint arXiv:1910.11728},
  year   = {2019}
}