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The Hausdorff Dimension is Convex on the Left Side of 1/4

  • Ludwik Jaksztas (a1)

Abstract

Let d(c) denote the Hausdorff dimension of the Julia set Jc of the polynomial fc (z) = z 2 +c. The function cd(c) is real-analytic on the interval (–3/4, 1/4), which is in the domain bounded by the main cardioid of the Mandelbrot set. We prove that the function d is convex close to 1/4 on the left side of it.

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