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 . 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}
}