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

• Date: 2010
• Main Authors: Maksimenko, S. I., Максименко, С. І.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2895
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 poin...