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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 pc(z)=z2+c with c∈[−2,2];
  3. verification of the conjecture of Ludwik Jaksztas and Michel Zinsmeister that the Hausdorff dimension of the Julia set of pc(z) is a C1-smooth function of the real parameter c∈(cF,−3/4), where cF=−1.401155189… 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