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Differentiable structures of central Cantor sets
Published online by Cambridge University Press: 12 April 2001
Abstract
Central Cantor sets form a class of symmetric Cantor sets of the real line. Here we give a complete characterization of the $C^{k + \alpha}$ regularity of these Cantor sets. We also give a classification of central Cantor sets up to global and local diffeomorphisms. Examples of central Cantor sets with special dynamical and measure-theoretical properties are also provided. Finally, we calculate the fractal dimensions of an arbitrary central Cantor set.
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- 1997 Cambridge University Press
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