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

Genadi Levin*, Grzegorz Świa̧tek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)421-424
Number of pages4
JournalComptes Rendus Mathematique
Volume339
Issue number6
DOIs
StatePublished - 15 Sep 2004

Bibliographical note

Funding Information:
E-mail addresses: levin@math.huji.ac.il (G. Levin), swiatek@math.psu.edu (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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