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Avila, Artur; Lyubich, Mikhail (2022). Lebesgue measure of Feigenbaum Julia sets. Annals of Mathematics. Second Series, 195(1):1-88.
We construct Feigenbaum quadratic-like maps with a Julia set of positive Lebesgue measure. Indeed, in the quadratic family Pc:z↦z2+c the corresponding set of parameters c is shown to have positive Hausdorff dimension. Our examples include renormalization fixed points, and the corresponding quadratic polynomials in their stable manifold are the first known rational maps for which the hyperbolic dimension is different from the Hausdorff dimension of the Julia set.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Uncontrolled Keywords: | Statistics, Probability and Uncertainty, Mathematics (miscellaneous) |
| Language: | English |
| Date: | 2022 |
| Deposited On: | 26 Apr 2022 12:39 |
| Last Modified: | 27 Dec 2024 02:39 |
| Publisher: | Mathematical Sciences Publishers |
| ISSN: | 0003-486X |
| OA Status: | Green |
| Free access at: | Publisher DOI. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.4007/annals.2022.195.1.1 |
| Related URLs: | https://arxiv.org/abs/1504.02986 |
| Other Identification Number: | MR4358413 |
Avila, Artur