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Results tagged with complex-dynamics
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user 3621
Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
25
votes
2
answers
1k
views
Exponential towers of $i$'s
It's well known that the expression $i^i$ takes on an infinite set of values if we understand $w^z$ to mean any number of the form $\exp (z (\ln w + 2 \pi i n))$ where $\ln$ is a branch of the natural …
- 19.7k
9
votes
1
answer
348
views
Tiling the plane with finitely many congruent pieces
Suppose $A_1,\dots,A_n$ are measurable subsets of the plane that are all related by rigid motions such that $|(A_1 \cup \dots \cup A_n)^c| = 0$ and $|A_i \cap A_j| = 0$ for all $1 \leq i < j \leq n$, …
- 19.7k