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April 2020 Periodic flows with global sections
Khadija Ben Rejeb
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Ark. Mat. 58(1): 39-56 (April 2020). DOI: 10.4310/ARKIV.2020.v58.n1.a3


Let $G = \lbrace h_t \; \vert \; t \in \mathbb{R} \rbrace$ be a continuous flow on a connected $n$-manifold $M$. The flow $G$ is said to be strongly reversible by an involution $\tau$ if $h_{-t} = \tau h_t \tau$ for all $t \in \mathbb{R}$, and it is said to be periodic if $h_s = $ identity for some $s \in \mathbb{R}^\ast$. A closed subset $K$ of $M$ is called a global section for $G$ if every orbit $G(x)$ intersects $K$ in exactly one point. In this paper, we study how the two properties “strongly reversible” and “has a global section” are related. In particular, we show that if $G$ is periodic and strongly reversible by a reflection, then $G$ has a global section.


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Khadija Ben Rejeb. "Periodic flows with global sections." Ark. Mat. 58 (1) 39 - 56, April 2020.


Received: 23 February 2019; Revised: 14 July 2019; Published: April 2020
First available in Project Euclid: 16 January 2021

Digital Object Identifier: 10.4310/ARKIV.2020.v58.n1.a3

Primary: ‎37B05‎ , 37B20 , 54H20‎ , 57S05 , 57S10

Keywords: global section , periodic flow , reflection , strongly reversible

Rights: Copyright © 2020 Institut Mittag-Leffler


Vol.58 • No. 1 • April 2020
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