Weak Closure Theorem for Double Staircase Actions
  We introduce a double staircase construction $T$ and show that the weak closure of $\{T^n\}$ is $\{\int, 2^{-m}T^n+(1-2^{-m})\int \ : m\in\N,\ n\in \Z\}.$ 
V.V.Ryzhikov
math.DS