Dynamics of neighborhoods of points under a continuous mapping of an interval

• Date: 2005
• Main Authors: Romanenko, Ye. Yu., Романенко, Е. Ю.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3705
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $\{ I, f Z^{+} \}$ be a dynamical system induced by the continuous map $f$ of a closed bounded interval $I$ into itself. In order to describe the dynamics of neighborhoods of points unstable under $f$, we suggest a notion of $\varepsilon \omega - {\rm set} \omega_{f, \varepsilon}(x)$ of a point...