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Applications of Dynamical Systems Theory to Fractals: A Study of Cookie-Cutter Cantor Sets

机译：动力系统理论在分形中的应用 - 曲奇切割器康托尔集的研究

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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. (Copyright (c) 1989 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)

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作者
Bedford, T.;
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年度 1989
页码 p.1-46
总页数 46
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Geometry ; Entropy ; Set theory ; Flow;

机译：几何;熵;集合论;流动;

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2. Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems [J] . Fan Aihua, Liao Lingmin, Wu Meng Mathematische Zeitschrift . 2018,第1a2期

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3. CPW-fed slotted CANTOR Set fractal antenna for WiMAX and WLAN applications [J] . Reha Abdelati, El Amri Abdelkebir, Benhmammouch Othmane, International Journal of Microwave and Wireless Technologies . 2017,第4期

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7. Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems [O] . Fan, Ai-Hua, Liao, Lingmin, Wu, Meng 2016

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Applications of Dynamical Systems Theory to Fractals: A Study of Cookie-Cutter Cantor Sets

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