区间动力学中的高阶Schwarzian导数
Higher order Schwarzian derivatives in interval dynamics
摘要：
本文引入了与单调矩阵函数理论密切相关的高阶Schwarzian导数的无穷序列。将经典的Koebe引理推广到具有一定阶正Schwarzian导数的映射，得到了高阶导数的控制。对于一个大类的多峰区间映射，我们证明了所有的逆分支的第一返回映射到足够小的邻域的临界值有其高阶Schwarzian导数积极的任何给定的顺序。
英文摘要：
We introduce an infinite sequence of higher order Schwarzian derivatives closely related to the theory of monotone matrix functions. We generalize the classical Koebe lemma to maps with positive Schwarzian derivatives up to some order, obtaining control over derivatives of high order. For a large class of multimodal interval maps we show that all inverse branches of first return maps to sufficiently small neighbourhoods of critical values have their higher order Schwarzian derivatives positive up to any given order.
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