Density of fiberwise orbits in minimal iterated function systems on the circle

摘要

We study the minimality of almost every orbital branch of minimal iteratedfunction systems (IFSs). We prove that this kind of minimality holds forforward and backward minimal IFSs generated by orientation-preservinghomeomorphisms of the circle. We provide new examples of iterated functionssystems where this behavior persists under perturbation of the generators.