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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.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\…
math.DS2015
Local dimensions of measures of finite type
Kathryn E. Hare, Kevin G. Hare, Kevin R. Matthews
We study the multifractal analysis of a class of equicontractive, self-similar measures of finite type, whose support is an interval. Finite type is a property weaker than the open…