Kernel of a map of a shift along the orbits of continuous flows
Let $F: M × R → M$ be a continuous flow on a topological manifold $M$. For every subset $V ⊂ M$, we denote by $P(V)$ the set of all continuous functions $ξ: V → R$ such that $F(x,ξ(x)) = x$ for all $x ∈ V$. These functions vanish at nonperiodic points of the flow, while their values at periodic points are integer multiples of the corresponding periods (in general, not minimal). In this paper, the structure of $P(V)$ is described for an arbitrary connected open subset $V ⊂ M$.
English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 5, pp 748-757.
Citation Example: Maksimenko S. I. Kernel of a map of a shift along the orbits of continuous flows // Ukr. Mat. Zh. - 2010. - 62, № 5. - pp. 651–659.