4.3: Spiral structures in the Julia sets
- Page ID
- 101398
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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.
Next we can investigate stability of fixed points and period 2 orbit of quadratic mappings analytically.