Julia sets and self-similar sets (Q1314682)
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scientific article; zbMATH DE number 503649
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Julia sets and self-similar sets |
scientific article; zbMATH DE number 503649 |
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Julia sets and self-similar sets (English)
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19 October 1994
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The paper establishes relationships between self-similar sets and Julia sets. The main result states the condition for a self-similar set to be homeomorphic to the Julia set for some polynomial map. It is known that for some polynomial map, under some conditions, Julia sets are self-similar and therefore can be defined by iterated function systems introduced by Hutchinson. The paper shows that a given invertible postcritically finite self-similar set is homeomorphic to the Julia set for some polynomial map.
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fractal
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symbolic dynamics
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self-similar sets
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Julia sets
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postcritically finite
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