Kernel of a map of a shift along the orbits of continuous flows

  • S. I. Maksimenko

Abstract

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 $V ⊂ M$.
Published
25.05.2010
How to Cite
MaksimenkoS. I. “Kernel of a Map of a Shift Along the Orbits of Continuous Flows”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 5, May 2010, pp. 651–659, https://umj.imath.kiev.ua/index.php/umj/article/view/2895.
Section
Research articles