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Quantitative recurrence properties in conformal iterated function systems. (English) Zbl 1319.11050

A quantitative form of Poincaré recurrence is shown for conformal iterated function systems that include \(b\)-adic expansions, continued fractions, and certain dynamical systems defined on fractal sets. One of the applications of these results to Diophantine approximation gives a partial answer to a question of K. Mahler [Bull. Aust. Math. Soc. 29, 101–108 (1984; Zbl 0517.10001)].

MSC:

11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
37F35 Conformal densities and Hausdorff dimension for holomorphic dynamical systems
28A80 Fractals

Citations:

Zbl 0517.10001
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References:

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