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math.DS2020
A non-Borel special alpha-limit set in the square
Steve Jackson, Bill Mance, Samuel Roth
We consider the complexity of special -limit sets, a kind of backward limit set for non-invertible dynamical systems. We show that these sets are always analytic, but not necess…
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…