Upper and lower Hausdorff dimension estimates for invariant sets of \(k-1\)-endomorphisms (Q2718015)
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scientific article; zbMATH DE number 1606234
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Upper and lower Hausdorff dimension estimates for invariant sets of \(k-1\)-endomorphisms |
scientific article; zbMATH DE number 1606234 |
Statements
13 June 2002
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Hausdorff dimension
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invariant sets
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Julia sets
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quadratic maps
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0.9850549
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0.92866546
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0.9230515
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0.91439486
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0.91314507
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0.9116897
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0.9115936
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0.90985376
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0.90789056
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Upper and lower Hausdorff dimension estimates for invariant sets of \(k-1\)-endomorphisms (English)
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This paper is devoted to the upper and lower Hausdorff dimension estimates for invariant sets of a special class of non-injective maps. These estimations are given in terms of the singular values of the tangent map. Note that the upper and lower dimension estimates for \(k-1\)-endomorphisms can be applied to Julia sets of quadratic maps on the complex plane.NEWLINENEWLINENEWLINESee also the author's paper in Nonlinearity 13, 1425-1438 (2000; Zbl 0978.37038).
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