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math.DS2016
Local dimensions of measures of finite type on the torus
Kathryn E. Hare, Kevin G. Hare, Kevin R. Matthews
The structure of the set of local dimensions of a self-similar measure has been studied by numerous mathematicians, initially for measures that satisfy the open set condition and,…
math.CA2016
Assouad dimensions of complementary sets
Ignacio Garcia, Kathryn Hare, Franklin Mendivil
Given a positive, decreasing sequence whose sum is , we consider all the closed subsets of such that the lengths of their complementary open intervals are in one to…
math.DS2016
Local dimensions of measures of finite type II - Measures without full support and with non-regular probabilities
Kathryn E. Hare, Kevin G. Hare, Michael Ka Shing Ng
Consider a sequence of linear contractions and probabilities with . We are interested in the self-similar measure $μ=\sum p_{j}μ\…