Spiral structures in the Julia sets
It is evident, that if φ = 2π m/n + δ,
δ « 1, then mapping
zk = f ok(z∗ +
ε) ~ z∗ + |λ| k
generates spiral structures in the neighbourhood of the fixed point
z∗ . Some of these spirals are shown below.
Next we can investigate stability of fixed points and period 2 orbit
of quadratic mappings analytically.
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updated 12 Sep 2013