The zero locus of the Green's function on C² for one-dimensional complex dynamics

A rational map in one variable can be considered as a homogeneous polynomial on C². Then we can define the Green's function, which is invariant under S¹-action. Hence It is defined in C²/S¹ ≅ R³. The 3D objects below are the zero locus of the Green's function for each dynamics.

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quadratic polynomials z²+c
- c=0.25 (cauliflower)
  - STL files:
    - low resolution (2.4M)
    - middle resolution (5.5M)
    - high resolution (18M)
  - OBJ file with texture (21M)
- c=-1 (basilica)
  - STL files:
    - low resolution (2.4M)
    - middle resolution (5.6M)
    - high resolution (27M)
  - OBJ file with texture (21M)
- c=i (dendrite)
  - STL files:
    - low resolution (3.0M)
    - middle resolution (6.6M)
    - high resolution (24M)
  - OBJ file with texture (25M)
quadratic rational map with period 2 and 3 superattracting cycles
- OBJ file with texture (27M)
quadratic rational map with period 3 and 4 superattracting cycles
- OBJ file with texture (27M)
quadratic rational map 1-1/z²
- OBJ file with texture (27M)
quadratic Lattès map
- STL files:
  - high resolution (27M)

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The zero locus of the Green's function on C2 for one-dimensional complex dynamics

The zero locus of the Green's function on C² for one-dimensional complex dynamics