On Lebesgue measure and Hausdorff dimension of Julia sets of real periodic points of renormalization
Volume 68 / 2020
Bulletin Polish Acad. Sci. Math. 68 (2020), 151-168
MSC: Primary 37F25; Secondary 37F35.
DOI: 10.4064/ba210406-10-4
Published online: 20 April 2021
Abstract
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.
