A parameterization of the period $3$ hyperbolic components of the Mandelbrot set
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- by Dante Giarrusso and Yuval Fisher PDF
- Proc. Amer. Math. Soc. 123 (1995), 3731-3737 Request permission
Abstract:
We demonstrate that the period 3 hyperbolic components of the Mandelbrot set consist of the image of the unit disk by the maps \[ - \frac {7}{4} - \frac {{20}}{9}{\left [ {\sinh \left ( {\omega (z) + \frac {{2k\pi i}}{3}} \right ) - \frac {1}{{4\sqrt 5 }}} \right ]^2},\] with \[ \omega (z) = \frac {1}{3}{\operatorname {Arcsinh}}\left ( {\frac {{88 - 27z}}{{80\sqrt 5 }}} \right ),\] for $k = 0,1,2$.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3731-3737
- MSC: Primary 30D05; Secondary 30C10
- DOI: https://doi.org/10.1090/S0002-9939-1995-1301497-3
- MathSciNet review: 1301497