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Results tagged with complex-dynamics
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user 80790
Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
1
vote
1
answer
444
views
Formal group law and Koenigs function conjecture?
Let $f(x,y)$ be a symmetric real function and a formal group law
$$G(x + y) = f(G(x),G(y)). \tag{1}$$
Consider the equation
$$ h(2x) = f(h(x),h(x)) = A(h(x)). \tag{2}$$
This equation has many solu …
- 769
1
vote
0
answers
471
views
The mysterious numbers $ \frac{13}{20} $ and $20$?
Let $g(x) = x^6 - 30 x $
Let $h(x) = x^6 $
Let $f(x) = x^2 - 2 $
Let $r$ be a reduced fraction $0 < \frac{p}{q} < 2 $ with integers $p,q > 1$
Let $f_{n+1}(x) = f(f_n(x)) = f_n(f(x)) , f_0(x) = x$ …
- 769
8
votes
1
answer
491
views
$f(f(z)) = z , f(\exp(z)) = \exp(f(z)) $?
While talking about tetration with my friend the following idea (re)occured.
$$f(f(z)) = z ,\quad f(\exp(z)) = \exp(f(z)) \tag{A}\label{A}$$
or variations of it like the weaker
$$f(f(f(f(z)))) = z ,\q …
- 769