论文标题
平面紧凑型和理性朱莉娅套装的模型
A model for planar compacta and rational Julia sets
论文作者
论文摘要
Peano Commactum是一个紧凑的度量空间，具有局部连接的组件，因此其中最多有限的直径大于任何固定数字C> 0。鉴于在扩展的复合平面中的压缩k，众所周知，k上最优质的上半连续分解为subcontinua，因此所产生的商空间是Peano Compactum。我们称这种分解为k的核心分解与peano商及其k的元素原子。我们表明，对于任何扩展复合平面的分支覆盖f的f，对于k的任何原子d，d下的d原子在f下的预先映射在f下有限很多，每个成分都是k下k的原子的一个原子。由于理性功能是分支覆盖物，因此我们的结果扩展了较早的函数，这些功能仅限于更有限的情况，要求f是多项式，而k在f下完全不变。
A Peano compactum is a compact metric space having locally connected components such that at most finitely many of them are of diameter greater than any fixed number C>0. Given a compactum K in the extended complex plane, it is known that there is a finest upper semi-continuous decomposition of K into subcontinua such that the resulting quotient space is a Peano compactum. We call this decomposition the core decomposition of K with Peano quotient and its elements atoms of K. We show that for any branched covering f of the extended complex plane onto itself and for any atom d of K, the preimage of d under f has finitely many components each of which is an atom of the preimage of K under f. Since rational functions are branched coverings, our result extends earlier ones that are restricted to more limited cases, requiring that f be a polynomial and K completely invariant under f.
