Overlapping Iterated Function Systems from the Perspective of Metric Number Theory Daniela Drescher Christopher Burns

Christopher Burns

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Overlapping Iterated Function Systems from the Perspective of Metric Number Theory Daniela Drescher Christopher BurnsIn this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation which shows that for a family of limsup sets, their Lebesgue measure is determined by the convergence or divergence of naturally occurring volume sums. For many parameterised families of overlapping iterated function systems, we prove that a typical member will exhibit