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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A Mandelbrot set whose boundary is piecewise smooth


Authors: M. F. Barnsley and D. P. Hardin
Journal: Trans. Amer. Math. Soc. 315 (1989), 641-659
MSC: Primary 58F08; Secondary 30D05
DOI: https://doi.org/10.1090/S0002-9947-1989-1011232-6
MathSciNet review: 1011232
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Abstract: It is proved that the Mandelbrot set associated with the pair of maps $ {w_{1,2}}:{\mathbf{C}} \to {\mathbf{C}}, {w_1}(z) = sz + 1, {w_2}(z) = {s^\ast }z - 1$, with parameter $ s \in {\mathbf{C}}$, is connected and has piecewise smooth boundary.


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DOI: https://doi.org/10.1090/S0002-9947-1989-1011232-6
Article copyright: © Copyright 1989 American Mathematical Society