Complementary components to the cubic principal hyperbolic domain
Complementary components to the cubic principal hyperbolic domain
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三次主双曲域的互补分量
DOI：
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发表时间：
2014
影响因子：
1
通讯作者：
V. Timorin
中科院分区：
文献类型：
--
作者：
A. Blokh;L. Oversteegen;R. Ptacek;V. Timorin
本文研究了三次主双曲域及其与所有三次多项式空间的切片的交mathcal{P}_lambda $的闭性，该空间的不动点由乘子$lambda$在$0$定义。本文证明了$mathcal{F}_dasetminusmathcal {P}_lambda$的任何有界域$mathcal{W}$都由具有连通Julia集$J（f）$的$J$-稳定多项式$f$组成，并且是Siegel捕获型的（则$fin mathcal{W}$在$0$附近有一个不变Siegel域$U$和另一个Fatou域$V$使得$f $|_V$是二对一的且$f^k（V）=U$（对于某些$k>0$）或具有奇异型（则$fin mathcal{W}$的至少一个临界点属于$J（f）$，集合$J（f）$具有正的勒贝格测度，且带有不变线域）。
We study the closure of the cubic Principal Hyperbolic Domain and its intersection $mathcal{P}_lambda$ with the slice $mathcal{F}_lambda$ of the space of all cubic polynomials with fixed point $0$ defined by the multiplier $lambda$ at $0$. We show that any bounded domain $mathcal{W}$ of $mathcal{F}_lambdasetminusmathcal{P}_lambda$ consists of $J$-stable polynomials $f$ with connected Julia sets $J(f)$ and is either of emph{Siegel capture} type (then $fin mathcal{W}$ has an invariant Siegel domain $U$ around $0$ and another Fatou domain $V$ such that $f|_V$ is two-to-one and $f^k(V)=U$ for some $k>0$) or of emph{queer} type (then at least one critical point of $fin mathcal{W}$ belongs to $J(f)$, the set $J(f)$ has positive Lebesgue measure, and carries an invariant line field).