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Results tagged with complex-dynamics
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user 1056
Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
2
votes
0
answers
54
views
Integral curves of rational vector fields and approximations
The following is the formal statement of a conjecture that feels almost obvious, but I cannot find a reference for it. The idea is that one can obtain the integral curves of a vector field $V(z)$ by l …
- 15.8k
19
votes
2
answers
3k
views
Is there some known way to create the Mandelbrot set (the boundary), with an iterated functi...
Is there some known way to create the Mandelbrot set (the boundary),
with an iterated function system (IFS)?
Julia sets can be formed by iterating the two functions $z \mapsto \pm \sqrt{z-c},$
and th …
- 15.8k
10
votes
1
answer
415
views
Convex Julia sets
Consider the classical Julia set $J_f$ associated with $f(z)=z^2+c$.
Since $J_c$ is completely invariant,
we know that $f^{-1}(J_f) \subseteq J_f$.
Now, let $H_f$ be the convex hull of $J_f$.
Is it t …
- 15.8k