Fractals/Iterations in the complex plane/julia/interior
" Stable orbits of polynomials may :
- converge to a (super)-attracting fixed point,
- (coverge) to a parabolic fixed point (where the multiplier is a root of unity),
- belong to a rotation domain (a simply connected domain on which the dynamics is conjugate to a rotation)." Lasse Rempe-Gillen [1]
Local discrete complex dynamics
edit - attracting : hyperbolic dynamics
- superattracting : the very fast ( = exponential) convergence to periodic cycle ( fixed point )
- parabolic component = slow ( lazy ) dynamics = slow ( exponential slowdown) convergence to parabolic fixed point ( periodic cycle)
- Siegel disc component = rotation around fixed point and never reach the fixed point
When Julia set is disconnected ther is no interior of Julia set ( critical fixed point is repelling ( or attracting to infinity)