Period functions for C^0- and C^1-flows - Maksimenko, S. I. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
Let F: M×R→M be a continuous flow on a manifold M, let V ⊂ M be an open subset, and let ξ: V→R be a continuous function. We say that ξ is a period function if F(x, ξ(x)) = x for all x ∈ V. Recently, for any open connected subset V ⊂ M; the author has described the structure of the set P(V) of all period functions on V. Assume that F is topologically conjugate to some C^1-flow. It is shown in this paper that, in this case, the period functions of F satisfy some additional conditions that, generally speaking, are not satisfied for general continuous flows.