Complex Dynamics

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4 domain-specific abstractions whose origin domain is Complex Dynamics.

• Classification of Fatou components — The dynamical classification of periodic stable regions of rational maps into attracting, parabolic, Siegel, Herman and related component types.
• Koenigs function — A holomorphic change of coordinate that conjugates iteration near an attracting or repelling fixed point to multiplication by the fixed-point multiplier.
• Mandelbrot set — The set of complex parameters for which iterating z squared plus c from zero remains bounded.
• Siegel Disc — Recognize a periodic Fatou component whose holomorphic first-return dynamics become an irrational rigid rotation after a biholomorphic change of coordinates.