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Abstract Let d(c) denote the Hausdorff dimension of the Julia set Jc of the polynomial fc (z) = z 2 +c. The function c ↦ d(c) is real-analytic on the… Click to show full abstract
Abstract Let d(c) denote the Hausdorff dimension of the Julia set Jc of the polynomial fc (z) = z 2 +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.
Keywords:
hausdorff dimension;
dimension convex;
convex left;
left side
Journal Title: Proceedings of the Edinburgh Mathematical Society
Year Published: 2017
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Journal Title: Proceedings of the Edinburgh Mathematical Society
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!