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

Artem Dudko
2021 Bulletin of the Polish Academy of Sciences Mathematics  
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. 2020 Mathematics
more » ... 0 Mathematics Subject Classification: Primary 37F25; Secondary 37F35.
doi:10.4064/ba210406-10-4 fatcat:om7d55li3bep3gfsn4vcxb64nu