单位球内的向后迭代
Backward iteration in the unit ball
摘要：
我们将考虑$\mathbb{C}^N$中单位球的解析自映射$f$的迭代。在1维情况下（即单位圆盘的自映射），关于这样的动力学已经有许多事实，我们将把其中一些推广到更高维。特别地，当$f$是双曲或椭圆的情况下，它将被证明，向后迭代序列与有界双曲的步骤收敛到一个点的边界上。这些点被称为边界排斥不动点，并具有几个很好的性质。在每个孤立边界排斥不动点处，我们也将通过解析交织映射构造$f$到自同构的（半）共轭。我们将以一些新的例子结束。
英文摘要：
We will consider iteration of an analytic self-map $f$ of the unit ball in $\mathbb{C}^N$. Many facts were established about such dynamics in the 1-dimensional case (i.e. for self-maps of the unit disk), and we will generalize some of them in higher dimensions. In particular, in the case when $f$ is hyperbolic or elliptic, it will be shown that backward-iteration sequences with bounded hyperbolic step converge to a point on the boundary. These points will be called boundary repelling fixed points and will possess several nice properties. At each isolated boundary repelling fixed point we will also construct a (semi) conjugation of $f$ to an automorphism via an analytic intertwining map. We will finish with some new examples.
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。
