6 citations · 24 across the 22 of their papers we have counts for
7 papers · 1 filter
Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions
Lior Fishman, Bill Mance, David Simmons +1
We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the non-autonomous dynamical system on the interval $[0…
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,…