论文标题
贝克域边界动力学的模型
A model for boundary dynamics of Baker domains
论文作者
论文摘要
我们考虑了先验的整个功能$ f（z）= z+e^{ - z} $，它具有二学位的双抛物线核心面包域$ U $，即一个不变的稳定组件，所有迭代均在本地均匀地融合到生物上，并为此，与之之间的超级距离之间的超级距离迭代迭代的距离转换为零倍数。从一般结果中可以知道，边界上的动力学是千古和经常性的，并且在$ \ partial u $中的点集中的轨道逃逸到Intimity的点具有零谐波测量。对于这个模型，我们表明结果更强，即这种逃逸集是非空的，它是由一些符号动力学编码的曲线组织的，其闭合恰好是$ \ partial u $。我们还证明，$ \ u $中的所有逃避点都不可从$ u $访问，而不是具有有界轨道的$ \ partial u $中的积分，这些轨道都是易于访问的。此外，排斥的定期点在@U中被证明是密集的，回答了一个张贴的问题Baranski，Fagella，Jarque和Karpinska。这些特征都不是为了偶然的抛物线面包师域而出现的。
We consider the transcendental entire function $ f(z)=z+e^{-z} $, which has a doubly parabolic Baker domain $U$ of degree two, i.e. an invariant stable component for which all iterates converge locally uniformly to infity, and for which the hyperbolic distance between successive iterates converges to zero. It is known from general results that the dynamics on the boundary is ergodic and recurrent and that the set of points in $\partial U$ whose orbit escapes to infity has zero harmonic measure. For this model we show that stronger results hold, namely that this escaping set is non-empty, it is organized in curves encoded by some symbolic dynamics, whose closure is precisely $\partial U$. We also prove that nevertheless, all escaping points in $\partial U$ are non-accessible from $U$, as opposed to points in $\partial U$ having a bounded orbit, which are all accessible. Moreover, repelling periodic points are shown to be dense in @U, answering a question posted Baranski, Fagella, Jarque and Karpinska. None of these features are known to occur for a general doubly parabolic Baker domain.
