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Let X = [0,1]. Given a non-uniformly contracting conformal iterated function system (IFS) and a family of positive Dini continuous potential functions , the triple system , under some conditions, determines uniquely a probability invariant measure, denoted by μ. In this paper, we study the pressure function of the system and multifractal structure of μ. We prove that the pressure function is Gateaux differentiable and the multifractal formalism holds, if the IFS has non-overlapping.
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