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The Hausdorff Dimension is Convex on the Left Side of 1/4
Published online by Cambridge University Press: 10 January 2017
Abstract
Let d(c) denote the Hausdorff dimension of the Julia set Jc of the polynomial fc(z) = z2 +c. The function c ↦ d(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.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 4 , November 2017 , pp. 911 - 936
- Copyright
- Copyright © Edinburgh Mathematical Society 2017
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