In 1965 Baker first considered the distribution of Julia sets of transcendental entire maps and proved that the Julia set of an entire map cannot be contained in any finite set of straight lines. In this paper we shall consider the distribution problem of Julia sets of meromorphic maps. We shall show that the Julia set of a transcendental meromorphic map with at most finitely many poles cannot be contained in any finite set of straight lines. Meanwhile, examples show that the Julia sets of meromorphic maps with infinitely many poles may indeed be contained in straight lines. Moreover, we shall show that the Julia set of a transcendental analytic self-map of C* can neither contain a free Jordan arc nor be contained in any finite set of straight lines.

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关于 Julia 全纯映射集的分布

1965 年，Baker 首先考虑了超越整图的 Julia 集的分布，并证明了整图的 Julia 集不能包含在任何有限直线集合中。在本文中，我们将考虑 Julia 亚纯映射集的分布问题。我们将证明，至多具有有限个极点的超越亚纯映射的 Julia 集不能包含在任何有限直线集内。同时，例子表明具有无限多个极点的 Julia 亚纯映射集可能确实包含在直线中。此外，我们将证明 C* 的先验解析自映射的 Julia 集既不能包含自由 Jordan 弧，也不能包含在任何有限直线集合中。