论文标题
区分端点集与ERDS空间
Distinguishing endpoint sets from Erdős space
论文作者
论文摘要
我们证明，$ f（z）= \ exp（z）-1 $的所有端点的集合在$ f $的迭代中逃到无限的$ f $ ns the Rational Hilbert Space $ \ Mathfrak E $并不是同型。作为推论，我们表明\ Mathbb c $的所有点$ z \的集合的轨道逃脱到$ \ infty $，或者吸引到$ 0 $。我们将这些结果扩展到指数家族中的许多其他功能。
We prove that the set of all endpoints of the Julia set of $f(z)=\exp(z)-1$ which escape to infinity under iteration of $f$ is not homeomorphic to the rational Hilbert space $\mathfrak E$. As a corollary, we show that the set of all points $z\in \mathbb C$ whose orbits either escape to $\infty$ or attract to $0$ is path-connected. We extend these results to many other functions in the exponential family.
