On the minimality of semigroup actions on the interval which are   $C^1$-close to the identity
  We consider semigroup actions on the interval generated by two attracting maps. It is known that if the generators are sufficiently $C^2$-close to the identity, then the minimal set coincides with the whole interval. In this article, we give a counterexample to this result under the $C^1$-topology. 
Katsutoshi Shinohara
math.DS