不变圆与余维1 Bottcher函数的超稳定流形
Superstable manifolds of invariant circles and co-dimension 1 Bottcher functions
摘要：
考虑了支配亚纯自映射$f: X -rightarrow X$的情形，其中$X$是维数为$n > 1$的紧致Kähler流形.假设存在一个嵌入的$\mathbb{P}^1$拷贝，它在$f$下是不变的，并且$f$是全纯的，并且在某个邻域内具有度为$a$的横向超吸引。假设限定于这条线的$f$由$z\mapsto z^b$给出，得到不变圆$S$。证明了若$a \geq b$，则局部稳定流形$W^s_\loc(S)$是实解析流形.事实上，我们陈述并证明了一个合适的本地化版本，可以在更广泛的背景下使用。然后，我们表明，条件$a \geq b$不能放松，而不增加额外的假设，提出两个例子与$a < b$的$W^s_\loc(S)$是不是真正的分析在附近的任何一点。
英文摘要：
We consider the situation of a dominant meromorphic self-map $f: X -rightarrow X$, where $X$ is a compact Kähler manifold of dimension $n > 1$. Suppose there is an embedded copy of $\mathbb{P}^1$ that is invariant under $f$, with $f$ holomorphic and transversally superattracting with degree $a$ in some neighborhood. Suppose $f$ restricted to this line is given by $z\mapsto z^b$, with resulting invariant circle $S$. We prove that if $a \geq b$, then the local stable manifold $W^s_\loc(S)$ is real analytic. In fact, we state and prove a suitable localized version that can be useful in wider contexts. We then show that the condition $a \geq b$ cannot be relaxed without adding additional hypotheses by presenting two examples with $a < b$ for which $W^s_\loc(S)$ is not real analytic in the neighborhood of any point.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
