不动点附近的固定曲线
Fixed curves near fixed points
摘要：
设$H$是$\mathbb{R}$ -线性平面映射和$z\mapsto z^n$的合成.我们根据$\mathbb{R}$ -线性映射的参数和与某个有限Blaschke积相关联的度对$H$的动力学进行了分类.我们应用这种分类的情况下，$z_0$是一个不动点的平面拟正则映射与常数复膨胀在附近的$z_0$。特别地，我们发现有多少曲线被$f$固定并且在$z_0$着陆。
英文摘要：
Let $H$ be a composition of an $\mathbb{R}$-linear planar mapping and $z\mapsto z^n$. We classify the dynamics of $H$ in terms of the parameters of the $\mathbb{R}$-linear mapping and the degree by associating a certain finite Blaschke product. We apply this classification to this situation where $z_0$ is a fixed point of a planar quasiregular mapping with constant complex dilatation in a neighbourhood of $z_0$. In particular we find how many curves there are that are fixed by $f$ and that land at $z_0$.
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。
