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

2019/10/25 by Shi, Enhui
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.11728

Abstract

In this report, we first recall the Poincaré'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 \mathbb Z^d. Also, some groups that admit/admit no topologically transitive actions on the line are determined.

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