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arXiv 1907.09366math.CVmath.DS
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Denjoy-Wolff定理的稳定性

Stability of the Denjoy-Wolff Theorem

Argyrios Christodoulou, Ian Short

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10 pages, 1 figure
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摘要：

Denjoy-Wolff定理是复动力学中的一个基本结果，它描述了单位圆盘$\mathbb{D}$的全纯自映射$f$的迭代序列的动力学行为.对于$n=1,2,\dotsc$，非自治动力系统$F_n=f_n\circ f_{n-1} \circ \dots \circ f_1$和$G_n=g_1\circ g_{2} \circ \dots \circ g_n$的理解要少得多，其中$f_i$和$g_j$是$\mathbb{D}$的全纯自映射。在这里，我们获得了一个透彻的了解，这样的系统$(F_n)$和$(G_n)$的假设下，$f_n\to f$和$g_n\to f$。我们确定当动态的$(F_n)$和$(G_n)$镜像的$(f^n)$，指定的Denjoy-Wolff定理，从而提供洞察到的稳定性的Denjoy-Wolff定理扰动下的地图$f$。

英文摘要：

The Denjoy-Wolff theorem is a foundational result in complex dynamics, which describes the dynamical behaviour of the sequence of iterates of a holomorphic self-map $f$ of the unit disc $\mathbb{D}$. Far less well understood are nonautonomous dynamical systems $F_n=f_n\circ f_{n-1} \circ \dots \circ f_1$ and $G_n=g_1\circ g_{2} \circ \dots \circ g_n$, for $n=1,2,\dotsc$, where $f_i$ and $g_j$ are holomorphic self-maps of $\mathbb{D}$. Here we obtain a thorough understanding of such systems $(F_n)$ and $(G_n)$ under the assumptions that $f_n\to f$ and $g_n\to f$. We determine when the dynamics of $(F_n)$ and $(G_n)$ mirror that of $(f^n)$, as specified by the Denjoy-Wolff theorem, thereby providing insight into the stability of the Denjoy-Wolff theorem under perturbations of the map $f$.

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。

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