8 citations · 16 across the 8 of their papers we have counts for
6 papers · 1 filter
Non-singular -actions: an ergodic theorem over rectangles with application to the critical dimensions
Anthony H. Dooley, Kieran Jarrett
We adapt techniques of Hochman to prove a non-singular ergodic theorem for -actions where the sums are over rectangles with side lengths increasing at arbitrary rates…
Sub-additive ergodic theorems for countable amenable groups
Anthony H. Dooley, Valentyn Ya. Golodets, Guohua Zhang
In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.
Local Entropy Theory of a Random Dynamical System
Anthony H. Dooley, Guohua Zhang
In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of or is replaced by the action of an infinite countable…
Topologies on the group of homeomorphisms of a Cantor set
Sergey Bezuglyi, Anthony H. Dooley, Jan Kwiatkowski
Let be the group of all homeomorphisms of a Cantor set . We study topological properties of and its subsets with respect to the uniform and weak $(τ_…
Topologies on the group of Borel automorphisms of a standard Borel space
Sergey Bezuglyi, Anthony H. Dooley, Jan Kwiatkowski
The paper is devoted to the study of topologies on the group Aut(X,B) of all Borel automorphisms of a standard Borel space . Several topologies are introduced and all possi…
The Rokhlin lemma for homeomorphisms of a Cantor set
Sergey Bezuglyi, Anthony H. Dooley, Konstantin Medynets
For a Cantor set , let denote the group of all homeomorphisms of . The main result of this note is the following theorem. Let be an aperiodic homeo…