Taylor series approximations to Julia set scaling functions (Q1199301)
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scientific article; zbMATH DE number 94093
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Taylor series approximations to Julia set scaling functions |
scientific article; zbMATH DE number 94093 |
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Taylor series approximations to Julia set scaling functions (English)
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16 January 1993
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Let \(J(c)\) be the Julia set of \(z^ 2+c\). \textit{W. D. Withers} [Chaotic dynamics and fractals, Notes Rep. Math. Sci. Engl. 2, 203-213 (1986; Zbl 0603.30029)] has shown that it is possible to expand \(J(c)\) in a Taylor series, that is, to make sense of the expression \[ J(c)=J(c_ 0)+(c-c_ 0)DJ(c_ 0)+{(c-c_ 0)^ 2\over 2} D^ 2 J(c_ 0)+\cdots. \] In this paper, this approach is taken to approximate the Ruelle-Bowen-Sinai and Feigenbaum scaling functions.
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scaling functions
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iteration
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Ruelle-Bowen-Sinai scaling functions
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Julia set
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Taylor series
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Feigenbaum scaling functions
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