Thickness of Julia sets of Feigenbaum polynomials with high order critical points

Genadi Levin; Grzegorz Świa̧tek

doi:10.1016/j.crma.2004.07.013

Thickness of Julia sets of Feigenbaum polynomials with high order critical points

Genadi Levin^*, Grzegorz Świa̧tek

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider unimodal polynomials with Feigenbaum topological type and critical points whose orders tend to infinity. It is shown that the hyperbolic dimensions of their Julia set go to 2; furthermore, that the Hausdorff dimensions of the basins of attraction of their Feigenbaum attractors also tend to 2. The proof is based on constructing a limiting dynamics with a flat critical point.

Original language	English
Pages (from-to)	421-424
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	339
Issue number	6
DOIs	https://doi.org/10.1016/j.crma.2004.07.013
State	Published - 15 Sep 2004

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (G. Levin), [email protected] (G. S´wiątek). 1 Both authors were supported by Grant No. 2002062 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. 2 Partially supported by NSF grant DMS-0245358.

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title = "Thickness of Julia sets of Feigenbaum polynomials with high order critical points",

abstract = "We consider unimodal polynomials with Feigenbaum topological type and critical points whose orders tend to infinity. It is shown that the hyperbolic dimensions of their Julia set go to 2; furthermore, that the Hausdorff dimensions of the basins of attraction of their Feigenbaum attractors also tend to 2. The proof is based on constructing a limiting dynamics with a flat critical point.",

author = "Genadi Levin and Grzegorz {\'S}wi{\c a}tek",

note = "Funding Information: E-mail addresses: [email protected] (G. Levin), [email protected] (G. S´wi{\c a}tek). 1 Both authors were supported by Grant No. 2002062 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. 2 Partially supported by NSF grant DMS-0245358.",

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AU - Świa̧tek, Grzegorz

N1 - Funding Information: E-mail addresses: [email protected] (G. Levin), [email protected] (G. S´wiątek). 1 Both authors were supported by Grant No. 2002062 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. 2 Partially supported by NSF grant DMS-0245358.

PY - 2004/9/15

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N2 - We consider unimodal polynomials with Feigenbaum topological type and critical points whose orders tend to infinity. It is shown that the hyperbolic dimensions of their Julia set go to 2; furthermore, that the Hausdorff dimensions of the basins of attraction of their Feigenbaum attractors also tend to 2. The proof is based on constructing a limiting dynamics with a flat critical point.

AB - We consider unimodal polynomials with Feigenbaum topological type and critical points whose orders tend to infinity. It is shown that the hyperbolic dimensions of their Julia set go to 2; furthermore, that the Hausdorff dimensions of the basins of attraction of their Feigenbaum attractors also tend to 2. The proof is based on constructing a limiting dynamics with a flat critical point.

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ER -

Thickness of Julia sets of Feigenbaum polynomials with high order critical points

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