# Henk Bruin, Matching for generalized $\beta$-transformations; Iztok Banič, The (weak) full projection property for inverse limits with upper semicontinuous bonding functions

Source: International topology seminar Ljubljana-Maribor-Zagreb

Topološki seminar **Ljubljana-Maribor-Zagreb** se bo sestal v soboto, 3.6.2017 v Ljubljani.

**Henk Bruin, Matching for generalized $\beta$-transformations**

Abstract: This talk is about the parameter space of a family of shifted $\beta$-transformations $T$ in regard to the property of “matching”. This means that at some iterate $T^n(0) = T^n(1)$, and it has a bearingon the invariant density of $T$. The prevalence of matching is proved under specific number-theoretic conditions: the slope $\beta$ is a(specifically quadratic) Pisot number.

**Iztok Banič, The (weak) full projection property for inverse limits with upper semicontinuous bonding functions **

Abstract: we give new results about the full projection property and the weak full projection property for inverse limits with upper semicontinuous functions. This solves several problems stated by W. T. Ingram