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Hausdorff dimension 2 for Julia sets of quadratic polynomials

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Abstract.

We consider families of quadratic polynomials which admit parameterisations in a neighbourhood of the boundary of the Mandelbrot set. We show how to find parameters such that the associated Julia sets are of Hausdorff dimension 2.

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Authors and Affiliations

  1. TU Clausthal, Institut für Theoretische Physik, D-38678 Clausthal-Zellerfeld, Germany (e-mail: Stefan.Heinemann@TU-Clausthal.DE) , , , , , , DE

    Stefan-M. Heinemann

  2. University of St Andrews, Mathematical Institute, St Andrews, KY16 9SS, Scotland (e-mail: bos@st-and.ac.uk) , , , , , , UK

    Bernd O. Stratmann

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  1. Stefan-M. Heinemann
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  2. Bernd O. Stratmann
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Received October 11, 1999 / Published online April 12, 2001

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Heinemann, SM., Stratmann, B. Hausdorff dimension 2 for Julia sets of quadratic polynomials. Math Z 237, 571–583 (2001). https://doi.org/10.1007/PL00004881

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  • DOI: https://doi.org/10.1007/PL00004881

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