Differentiable Structures on Fractal Like Sets, Determined by Intrinsic Scaling Functions on Dual Cantor Sets
There is an easy notion of differentiate structure on a topological space. In the case of an embedded Cantor set in the line the differentiate structure records the fine scale geometrical structure. We will discuss two examples from the theory of one dimensional smooth dynamical systems, namely Cantor sets dynamically defined by i) folding maps on the boundary of chaos,and by ii) smooth expanding maps.
KeywordsScaling Function Scaling FUNCT Ratio Function Difference Quotient Differentiable Structure
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