Geodesic
On Lebesgue measure and Hausdorff dimension of Julia sets of real periodic points of renormalization
Artem Dudko1
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland <a href="https://orcid.org/0000-0003-2706-3215">ORCID: 0000-0003-2706-3215</a>
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 68 (2020) no. 2, pp. 151-168

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ba210406-10-4
Keywords: sufficient condition julia set real analytic function which periodic point renormalization have hausdorff dimension nbsp condition verified numerically present results computer experiments suggesting condition satisfied real periodic points renormalization low periods results support conjecture real feigenbaum maps have julia sets hausdorff dimension nbsp

Artem Dudko 1

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland <a href="https://orcid.org/0000-0003-2706-3215">ORCID: 0000-0003-2706-3215</a> 
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Artem Dudko. On Lebesgue measure and Hausdorff dimension of Julia sets of real periodic points of renormalization. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 68 (2020) no. 2, pp. 151-168. doi: 10.4064/ba210406-10-4

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