Period functions for $\mathcal{C}^0$- and $\mathcal{C}^1$-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/2928
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 th...