Wandering Sets for a Class of Borel Isomorphisms of ...0,1).
Weak Closure Theorem fails for ℤ²-actions
We construct an example of a Morse ℤ²-action which has rank one and whose centralizer contains elements which cannot be weakly approximated by the transformations of the action.
Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary
Weak mixing of maps with bounded cutting parameter.
Weakly mixing transformations and the Carathéodory definition of measurable sets
Let 𝕋 denote the set of complex numbers of modulus 1. Let v ∈ 𝕋, v not a root of unity, and let T: 𝕋 → 𝕋 be the transformation on 𝕋 given by T(z) = vz. It is known that the problem of calculating the outer measure of a T-invariant set leads to a condition which formally has a close resemblance to Carathéodory's definition of a measurable set. In ergodic theory terms, T is not weakly mixing. Now there is an example, due to Kakutani, of a transformation ψ̃ which is weakly mixing but not strongly...