ON REGULAR CURVES HOMEOMORPHISMS WITHOUT PERIODIC POINTS
Aymen Daghar · HAL (Le Centre pour la Communication Scientifique Directe) · 2020
The purpose of this paper is to study the dynamic of regular curves homeomorphisms without periodic points. We show mainly that they behave similarly like circle's homeomorphisms without periodic points. For instance, we prove that they are extensions of irrational rotation of the circle via a monotone factor map collapsing proximal pairs and we prove also the absence of Li-Yorke pairs. Furthermore, we give a characterisation of minimal sets, in particular we get that the circle is the only regular curve admitting a minimal (or a transitive) Z-action. At the end of the paper, we give some counterexamples on rational curves.