Linearization problem on structurally finite entire functions
Linearization problem on structurally finite entire functions
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DOI：
10.2996/kmj/1123767015
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发表时间：
2004-08
影响因子：
0.6
通讯作者：
Y. Okuyama
中科院分区：
文献类型：
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作者：
Y. Okuyama
我们证明了如果一个1-双曲型结构有限整函数的$（p，q）$，$p\ge 1 $，是可线性化的在一个无理的中立不动点，那么它的乘子满足Brjuno条件.我们还证明了推广的Man 'e定理：如果一个整函数只有1000个临界点和渐近值，那么对于每一个这样的非扩张前向不变集，即Cremer圈或Siegel圆盘圈的边界，存在一个渐近值或一个回归临界点，使得它的前向轨道的导出集包含这个不变集.由此，自然产生了$n $-亚双曲性的概念。
We show that if a 1-hyperbolic structurally finite entire function of type $(p,q)$, $p\ge 1$, is linearizable at an irrationally indifferent fixed point, then its multiplier satisfies the Brjuno condition. We also prove the generalized Ma\~n\'e theorem; if an entire function has only finitely many critical points and asymptotic values, then for every such a non-expanding forward invariant set that is either a Cremer cycle or the boundary of a cycle of Siegel disks, there exists an asymptotic value or a recurrent critical point such that the derived set of its forward orbit contains this invariant set. From it, the concept of $n$-subhyperbolicity naturally arises.