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Results tagged with complex-dynamics
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user 26522
Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
6
votes
3
answers
338
views
Clustering of periodic points for a polynomial iteration of $\mathbb{C}$
Let $f : \mathbb{C} \to \mathbb{C}$ be a polynomial map of degree $q > 1$. Consider $E_n \subset \mathbb{C}$ the set of periodic points with period (dividing) $n$; generally, $|E_n| = q^n$. Since all …
- 13.8k
13
votes
0
answers
309
views
Diophantine approximation in the Julia set
Let $f : \mathbb{CP}^1 \to \mathbb{CP}^1$ be a rational map of degree $q > 1$; or just a quadratic binomial $z^2 + c$, if one prefers. The Julia set $J_f$ is the closure of the repelling periodic poin …
- 13.8k
9
votes
0
answers
320
views
Discriminants of Gleason's period-$n$ polynomials for the Mandelbrot set
Gleason's polynomials are the sequence of monic integer polynomials defined recursively by
$$
\prod_{d \mid n} G_d(c) = (((c^2+c)^2+c)^2+\cdots+c)^2+c \quad \quad \quad [\textrm{$n$ iterates}],
$$
for …
- 13.8k