Erdős Julia集合中的空间

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-07-15 DOI:10.1112/blms.70131

David S. Lipham

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引用次数: 0

摘要

我们证明了理性希尔伯特空间，即Erdős空间E $\mathfrak {E}$，在复杂动力学中通过ez−1$ E ^z-1$的迭代得到曲面。更准确地说，E $\mathfrak {E}$在拓扑上等价于Julia集合J(E z−1)$ J(E ^z-1)$的端点集合，其轨道在虚方向上趋于无穷。

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Erdős space in Julia sets

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Erdős space in Julia sets

We prove that the rational Hilbert space, known as the Erdős space $E$ , surfaces in complex dynamics via iteration of $e^{z} - 1$ . More precisely, $E$ is topologically equivalent to the set of endpoints of the Julia set $J (e^{z} - 1)$ whose orbits tend to infinity in the imaginary direction.