区间上双同态的增长间隙与光滑性
Growth Gap vs. smoothness for diffeomorphisms of the interval
摘要：
给定区间的一个自同态，考虑其第n次迭代的导数的一致范数。我们得到一个实数序列，称为增长序列。它的渐近行为是一个不变量，自然地出现在光滑动力学和几何的同构群。我们发现尖锐的估计增长序列的一个给定的超同态的模连续的衍生物。这些估计扩展了Polterovich和Sodin以及Borichev的先前结果。
英文摘要：
Given a diffeomorphism of the interval, consider the uniform norm of the derivative of its n-th iteration. We get a sequence of real numbers called the growth sequence. Its asymptotic behavior is an invariant which naturally appears both in smooth dynamics and in geometry of the diffeomorphisms groups. We find sharp estimates for the growth sequence of a given diffeomorphism in terms of the modulus of continuity of its derivative. These estimates extend previous results of Polterovich and Sodin, and Borichev.
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