It is evident, that if φ = 2π m/n + δ,
δ « 1, then mapping
zk = f ok(z∗ +
ε) ~ z∗ + |λ| k
eikφε generates spiral structures in the neighbourhood of the fixed point
z∗ . Some of these spirals are shown below.
wait
wait
0.0000 0.1000 2.5000 36ms
wait
Next we can investigate stability of fixed points and period 2 orbit
of quadratic mappings analytically.