Periodic flows with global sections

Abstract

Let G={ht | 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=τhtτ for all t∈R, and it is said to be periodic if hs = 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.