Poincare级数与指数映射的不稳定性
Poincare Series and instability of exponential maps
摘要：
我们将指数族的后奇异集的性质与稳定性问题联系起来。我们计算指数族的Ruelle算子的作用。证明了若该映射的渐近值是可和点且其轨道满足一定的拓扑条件，则该映射是不稳定的，因此在朱利亚集中不存在Beltrami微分.证明了如果后奇异集是紧集，则奇异值是可和的。
英文摘要：
We relate the properties of the postsingular set for the exponential family to the questions of stability. We calculate the action of the Ruelle operator for the exponential family. We prove that if the asymptotic value is a summable point and its orbit satisfies certain topological conditions, the map is unstable hence there are no Beltrami differentials in the Julia set. Also we show that if the postsingular set is a compact set, then the singular value is summable.
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