5 citations · 13 across the 8 of their papers we have counts for
12 papers
Descriptive complexity in Cantor series
Dylain Airey, Steve Jackson, Bill Mance
A Cantor series expansion for a real number with respect to a basic sequence , where , is a representation of the form $x=a_0 + \sum_{i=1}^\infty…
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…
A topological dynamical system with two different positive sofic entropies
Dylan Airey, Lewis Bowen, Frank Lin
A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations.…
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…
Some complexity results in the theory of normal numbers
Dylan Airey, Bill Mance, Steve Jackson
Let be the set of real numbers which are normal to base . A well-known result of H. Ki and T. Linton is that is -complete. We…
Normality of different orders for Cantor series expansions
Dylan Airey, Bill Mance
Let have the property that for each the set has asymptotic density . We prove that there exists a basic…
Normal number constructions for Cantor series with slowly growing bases
Dylan Airey, Bill Mance, Joseph Vandehey
Let be a sequence of bases with . In the case when the are slowly growing and satisfy some additional weak conditions, we provide a construct…
Normal equivalencies for eventually periodic basic sequences
Dylan Airey, Bill Mance
W. M. Schmidt, A. D. Pollington, and F. Schweiger have studied when normality with respect to one expansion is equivalent to normality with respect to another expansion. Following…
Normality preserving operations for Cantor series expansions and associated fractals part II
Dylan Airey, Bill Mance, Joseph Vandehey
We investigate how non-zero rational multiplication and rational addition affect normality with respect to -Cantor series expansions. In particular, we show that there exists a…
On the Hausdorff dimension of some sets of numbers defined through the digits of their -Cantor series expansions
Dylan Airey, Bill Mance
Following in the footsteps of P. Erdős and A. Rényi we compute the Hausdorff dimension of sets of numbers whose digits with respect to their -Cantor series expansions satisfy va…
Normality preserving operations for Cantor series expansions and associated fractals part I
Dylan Airey, Bill Mance
It is well known that rational multiplication preserves normality in base . We study related normality preserving operations for the -Cantor series expansions. In particular,…
Unexpected distribution phenomenon resulting from Cantor series expansions
Dylan Airey, Bill Mance
We explore in depth the number theoretic and statistical properties of certain sets of numbers arising from their Cantor series expansions. As a direct consequence of our main theo…