In this talk I will present an algorithm for estimating from below the Hausdorff dimensions of Julia sets for a wide class of holomorphic maps together with several applications, including:

1. a lower bound on the Hausdorff dimension of the Julia sets of several Feigenbaum polynomials;
2. a graph of a function estimating from below the Hausdorff dimension of the Julia sets of all quadratic polynomials $p_c (z) = z^2 +c$ with $c\in[-2,2]$;
3. verification of the conjecture of Ludwik Jaksztas and Michel Zinsmeister that the Hausdorff dimension of the Julia set of $p_c (z)$ is a $C^1$-smooth function of the real parameter $c\in(c_F ,-3/4)$, where $c_F =-1.401155189\ldots$ is the Feigenbaum parameter.

The talk is based on a joint work with Igors Gorbovickis and Warwick Tucker.
Meeting ID: 852 4277 3200 Passcode: 103121