We introduce a formalism for handling general spaces of hierarchical tilings, a category that
includes substitution tilings, Bratteli–Vershik systems, S-adic transformations, and multi …

We study the dynamic properties of rank-one ℤd actions as a function of the geometry of the
shapes of the towers generating the action. Some basic properties require only minimal …

For each n> 1, we construct explicitly a rigid weakly mixing rank-n transformation with
homogeneous spectrum of multiplicity n. The existence of such transformations was …

This is a survey of a recent progress related to the (C, F)-construction of funny rank-one
actions for locally compact groups. We exhibit a variety of examples and counterexamples …

A weakly mixing measure preserving action of a locally compact second countable group on
a standard probability space is called 2-fold near simple if every ergodic joining of it with …

Mixing (of all orders) rank-one actions T of the Heisenberg group H3 (R) are constructed.
The restriction of T to the center of H3 (R) is simple and commutes only with T. Mixing …

Let G be a countable direct sum of finite groups. We construct an uncountable family of
pairwise disjoint mixing (of any order) rank-one strictly ergodic free actions of G on a Cantor …

CUT-AND-STACK SIMPLE WEAKLY MIXING MAP WITH COUNTABLY MANY PRIME
FACTORS 0. Introduction Let T be an (invertible) transformation Page 1 PROCEEDINGS OF …

RANK-ONE FLOWS OF TRANSFORMATIONS WITH INFINITE ERGODIC INDEX 0. Introduction
In 1963 Kakutani and Parry discovered an interesti Page 1 PROCEEDINGS OF THE …

The article presents a study of the self-joinings of commutative actions with invariant
measure, focusing on the interaction with other systems and its arrangement in the …