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A remark on densities of hyperbolic dimensions for conformal iterated function systems with applications to conformal dynamics and fractal number theory. (English summary) Indag. Math. (N.S.) 17 (2006), no. 2, 311–317. Let X be a compact subset of RN and let ϕi: X → X be an injective contraction. Here i ∈ I and I is a finite or infinite set of indices. One can construct an iterated function system (X, Φ), where Φ = {ϕi}i∈I. The authors assume it to satisfy the open set condition and to be conformal (CIFS). Put ϕω = ϕi1 ◦ · · · ◦ ϕin, where ω = (i1,..., in) ∈ In, and Λ(Φ) = ⋂ ⋃ ϕω(int(X)). n∈N ω∈I n The main result of the paper is the main theorem which asserts that there exists a set H(Φ) of hyperbolic subsets of Λ(Φ) (i.e., limits of finite subsystems of (X, Φ)) such that the set is dense in the interval {dimH(S) | S ∈ H(Φ)

Year: 2011

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