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Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
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Representing a number close to 1 with a sum of reciprocals of natural numbers
For positive integers $n_1, \ldots, n_k$, let $H(n_1, \ldots, n_k)$ denote $1/n_1 + \ldots + 1/n_k$. Let $V(N)$ be the largest possible value of $H(n_1, \ldots, n_k)$ that is less than 1, subject to t …