On Lebesgue measure and Hausdorff dimension of Julia sets of real periodic points of renormalization

• Autorzy: Dudko Artem

Identyfikatory

DOI

10.4064/ba210406-10-4

• Języki publikacji: EN

Abstrakty

EN

We give a new sufficient condition for the Julia set of a real analytic function which is a periodic point of renormalization to have Hausdorff dimension less than 2. This condition can be verified numerically. We present results of computer experiments suggesting that this condition is satisfied for real periodic points of renormalization with low periods. Our results support the conjecture that all real Feigenbaum maps have Julia sets of Hausdorff dimension less than 2.

Słowa kluczowe

EN

renormalization; Feigenbaum maps; Julia set; Hausdorff dimension

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2020
• Tom: Vol. 68, no. 2
• Strony: 151--168
• Opis fizyczny: Bibliogr.21 poz., rys.

Twórcy

autor

Dudko Artem

• Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-656 Warszawa, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).