D. Airey

activity

20182020

collaborators

3 papers

math.LO2020

Descriptive complexity in Cantor series

Dylain Airey, Steve Jackson, Bill Mance

A Cantor series expansion for a real number $x$ with respect to a basic sequence $Q = (q_{1}, q_{2}, \dots)$ , where $q_{i} \geq 2$ , is a representation of the form $x=a_0 + \sum_{i=1}^\infty…

math.DS2019

Hotspot lemmas for non-compact spaces

Dylan Airey, Bill Mance

We extend the hotspot lemma, or Piatetskiĭ-Shapiro normality criterion, to dynamical systems on non-compact spaces. We build on the work of N. G. Moshchevitin and I. D. Shkredov, n…

math.DS2018

Borel complexity of sets of normal numbers via generic points in subshifts with specification

Dylan Airey, Steve Jackson, Dominik Kwietniak +1

We study the Borel complexity of sets of normal numbers in several numeration systems. Taking a dynamical point of view, we offer a unified treatment for continued fraction expansi…