Abstract
Cookie-cutter Cantor sets in the line are studied as simple examples of fractals which are invariant sets of dynamical systems. The topics covered are: the characterization of a cookie-cutter via a dynamical system or an iterated function system (i.f.s.); introduction of measure theoretic and topological entropy and comparison with the concept of dimension; Bowen’s formula for Hausdorff dimension; a flow canonically associated with a cookie-cutter Cantor set; the order two density of Hausdorff measure (a characterization of lacunarity); the multifractal spectrum for cookie-cutters; and, Sullivan’s classification theorem for cookie-cutters.
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Bedford, T. (1991). Applications of dynamical systems theory to fractals — a study of cookie-cutter Cantor sets. In: Bélair, J., Dubuc, S. (eds) Fractal Geometry and Analysis. NATO ASI Series, vol 346. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7931-5_1
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