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 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.

Contents   Previous: Local dynamics at a fixed point Next: Attracting fixed point and period 2 orbit
updated 12 Sep 2013