Évènement

Title: Density of Stable Interval Translation Mappings

Interval Translations Maps (ITM’s) are a natural generalization of the well-known Interval Exchange Transformations (IET’s), obtained by dropping the bijectivity assumption for IET’s. Each (irreducible) ITM is either of finite or infinite type, depending on its non-wandering set: it is a finite union of intervals for the finite type maps, and a Cantor set for the infinite type maps. One of the basic questions in the field is: How prevalent is either type of map in the parameter space?

In this talk, I will discuss a joint work with Sebastian van Strien and Kostya Drach in which we show that the set of finite type maps contains an open and dense subset of the parameter space. This is achieved by proving that the stable ITM’s, which are open and of finite type by definition, form a dense subset of the parameter space.