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[A selection of probabilistic renewal theorems and renewal theorems in symbolic dynamics are presented. The selected renewal theorems have been widely applied. Here, we will show how they can be utilised to solve problems in fractal geometry with particular focus on counting problems and the question of Minkowski measurability. The fractal sets we consider include self-similar and self-conformal sets as well as limit sets of graph-directed systems consisting of similarities and conformal mappings.]
Published: Mar 24, 2021
Keywords: Renewal theorem; Dependent interarrival times; Symbolic dynamics; Minkowski content; Counting problems in fractal geometry; Ruelle Perron-Frobenius theory; Primary: 60K05; 60K15; Secondary: 28A80; 28A75
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