消除负Schwarzian导数条件
Getting rid of the negative Schwarzian derivative condition
摘要：
在本文中，我们将证明在具有非平坦临界点的C^3单峰映射的情况下，关于负Schwarzian导数的假设是多余的。证明了以下定理：对于任何具有非平坦临界点的区间的C^3单峰映射，在临界值附近存在一个区间，使得到该区间的第一个入口映射具有负的Schwarzian导数。本文证明的另一个定理提供了有用的交比估计。因此，所有仅对具有负Schwarzian导数的单峰映射证明的定理可以很容易地推广。
英文摘要：
In this paper we will show that the assumption on the negative Schwarzian derivative is redundant in the case of C^3 unimodal maps with a nonflat critical point. The following theorem will be proved: For any C^3 unimodal map of an interval with a nonflat critical point there exists an interval around the critical value such that the first entry map to this interval has negative Schwarzian derivative. Another theorem proved in the paper provides useful cross-ratio estimates. Thus, all theorems proved only for unimodal maps with negative Schwarzian derivative can be easily generalized.
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