The topology of Julia sets for geometrically finite polynomials (Q1389920)
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scientific article; zbMATH DE number 1174360
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The topology of Julia sets for geometrically finite polynomials |
scientific article; zbMATH DE number 1174360 |
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The topology of Julia sets for geometrically finite polynomials (English)
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14 July 1998
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A rational map \(R\) is called geometrically finite if the intersection set of the closure of its postcritical set \(P_R\) and its Julia set \(J(R)\) is a finite set. In this paper, the author proves that for any geometrically finite polynomial \(f\), each component of \(J(f)\) is locally connected; and \(J(f)\) is a Cantor set if and only if each critical component of its filled-in Julia set is not periodic.
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Julia set
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geometrically finite polynomial
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