Dynamics of entire functions near the essential singularity
Dynamics of entire functions near the essential singularity
复制标题
本质奇点附近整个函数的动力学
DOI：
10.1017/s0143385700003655
复制
发表时间：
1986
影响因子：
0.9
通讯作者：
F. Tangerman
中科院分区：
文献类型：
--
作者：
R. Devaney;F. Tangerman
摘要我们证明了临界有限且满足一定增长条件的整函数在其Julia集中有“Cantor花束”。这些是Julia集的不变子集，它们同胚于Cantor集和线[0，∞）的乘积。花束中的所有曲线都趋向于相同方向的∞，并且映射的行为类似于Cantor集上的移位自同构。因此，可以完全分析这类映射在∞附近的动力学。在我们的方法适用的整个映射中，有exp（z），sin（z）和cos（z）。
Abstract We show that entire functions which are critically finite and which meet certain growth conditions admit ‘Cantor bouquets’ in their Julia sets. These are invariant subsets of the Julia set which are homeomorphic to the product of a Cantor set and the line [0, ∞). All of the curves in the bouquet tend to ∞ in the same direction, and the map behaves like the shift automorphism on the Cantor set. Hence the dynamics near ∞ for these types of maps may be analyzed completely. Among the entire maps to which our methods apply are exp (z), sin (z), and cos (z).