Abstract |
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For a sequence (cn) of
complex numbers we consider the quadratic polynomials
fcn(z) :=
z2 + cn and
the sequence (Fn) of iterates Fn :=
fcn
∘⋯∘fc1.
The Fatou set F(cn) is by
definition the set of all z
in C such
that (Fn) is normal in some neighbourhood of
z, while the complement of
F(cn) is
called the Julia set J(cn). The
aim of this article is to study geometric properties, Lebesgue
measure and Hausdorff dimension of the Julia set
J(cn)
provided that the sequence (cn) is
bounded.
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Authors
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Berkeley, California.