A topological characterization of periodic flows

Abstract

Let $G=\{h_t|t\in \mathbb{R}\}$ be a continuous flow of homeomorphisms of a connected n-manifold M. The flow G is called periodic if: for some real s>0, $h_s=identity$. A global section for a flow G is a closed subset K of M such that every orbit under G intersects K in exactly one point. In this paper, we give a topological characterization of periodic flows with global sections for $M={\mathbb{R}}^n$. Next, we consider periodic flows defined on any connected n-manifold M, and we give a similar local characterization.

Keywords:

• Flow of homeomorphisms
• periodic
• global section
• topologically conjugate
• flow of rotations

2000 Mathematics Subject Classification. MSC 2010::

• 37B05
• 57S05
• 57S10
• 54H20
• 37B20

Disclosure statement

No potential conflict of interest was reported by the author.