Periodic flows with global sections

Khadija Ben Rejeb Institute of Computer Science and Communication Techniques, University of Sousse, Hammam Sousse, Tunisia

Geometric Analysis and Geometric Topology mathscidoc:2203.15001

Arkiv for Matematik, 58, (1), 39-56, 2020.4
Let G={h_t|t∈ℝ} be a continuous flow on a connected n-manifold M. The flow G is said to be strongly reversible by an involution τ if h_{−t}=τh_tτ for all t∈ℝ, and it is said to be periodic if h_s= identity for some s∈ℝ^∗. 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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  title={Periodic flows with global sections},
  author={Khadija Ben Rejeb},
  booktitle={Arkiv for Matematik},
Khadija Ben Rejeb. Periodic flows with global sections. 2020. Vol. 58. In Arkiv for Matematik. pp.39-56.
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