7 citations · 10 across the 8 of their papers we have counts for
8 papers
A strongly aperiodic shift of finite type on the discrete Heisenberg group using Robinson tilings
Ayse A. Sahin, Michael Schraudner, Ilie Ugarcovici
We explicitly construct a strongly aperiodic subshift of finite type for the discrete Heisenberg group. Our example builds on the classical aperiodic tilings of the plane due to Ra…
The complexity threshold for the emergence of Kakutani inequivalence
Van Cyr, Aimee Johnson, Bryna Kra +1
We show that linear complexity is the threshold for the emergence of Kakutani inequivalence for measurable systems supported on a minimal subshift. In particular, we show that ther…
The Morse minimal system is nearly continuously Kakutani equivalent to the binary odometer
Andrew Dykstra, Ayse Sahin
Ergodic homeomorphisms and of Polish probability spaces and are evenly Kakutani equivalent if there is an orbit equivalence between full me…
Directional Recurrence for Infinite Measure Preserving Z^d Actions
Aimee S. A. Johnson, Ayse A. Sahin
We define directional recurrence for infinite measure preserving Z^d actions both intrinsically and via the unit suspension flow and prove that the two definitions are equivalent.…
Rudolph's Two-Step Coding Theorem and Alpern's Lemma for R^d Actions
Bryna Kra, Anthony Quas, Ayse Sahin
Rudolph showed that the orbits of any measurable, measure preserving action can be measurably tiled by rectangles and asked if this number of tiles is optimal f…
The structure and spectrum of Heisenberg odometers
Samuel Lightwood, Ayse A. Sahin, Ilie Ugarcovici
In recent work Cortez and Petite defined odometer actions of discrete, finitely generated and residually finite groups G. In this paper we focus on the case where G is the discrete…
The Z^d Alpern multi-tower theorem for rectangles: a tiling approach
Ayse A. Sahin
We provide a proof of the Alpern multi-tower theorem for Z^d actions. We reformulate the theorem as a problem of measurably tiling orbits of a Z^d action by a collection of rectang…
Dye's theorem in the almost continuous category
Andres del Junco, Ayse A. Sahin
We prove an almost continuous version of Dye's theorem: any two non-atomic probability measure preserving homeomorphisms of Polish spaces are almost continuously orbit equivalent.…