Growth of Groups and Diffeomorphisms of the Interval
Growth of Groups and Diffeomorphisms of the Interval
复制标题
群的增长和区间的微分同胚
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
A. Navas
中科院分区：
文献类型：
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作者：
A. Navas
摘要。证明了对于所有α > 0，每一有限生成的具有次指数增长区间的C1+α微分同态群几乎是幂零的。因此，不存在具有中间生长的C1+α区间差胚群。此外，我们通过给出一个C1反例来证明这个断言的C1+α正则性假设是必不可少的。
Abstract.We prove that, for all α > 0, every finitely generated group of C1+α diffeomorphisms of the interval with sub-exponential growth is almost nilpotent. Consequently, there is no group of C1+α interval diffeomorphisms having intermediate growth. In addition, we show that the C1+α regularity hypothesis for this assertion is essential by giving a C1 counter-example.