Khadija Ben Rejeb
university of Sousse , Hammam sousse, Tunisia
Higher School of Sciences and Technology of Hammam
Publications:
Rejeb K.
Strongly Reversible Flows on Connected Manifolds
2021, vol. 26, no. 6, pp. 742755
Abstract
Let $G = \{h_t \  \ t \in \mathbb R\}$ be a flow of homeomorphisms of a connected $n$manifold and let $L(G)$ be its limit set. The flow $G$ is said to be strongly reversed by a reflection $R$ if $h_{t} = R h_t R$ for all $t \in \mathbb R$. In this paper, we study the dynamics of positively equicontinuous strongly reversible flows. If $L(G)$ is nonempty, we discuss the existence of symmetric periodic orbits, and for $n=3$ we prove that such flows must be periodic. If $L(G)$ is empty, we show that $G$ positively equicontinuous implies $G$ strongly reversible and $G$ strongly reversible implies $G$ parallelizable with
global section the fixed point set $Fix(R)$.
