3 papers
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…
math.NT2010
On winning sets and non-normal numbers
Bill Mance
In \cite{SchmidtGames}, W. Schmidt proved that the set of non-normal numbers in base is a {\it winning set}. We generalize this result by proving that many sets of non-normal n…