生长和混合
Growth and mixing
摘要：
给定有限维紧度量测度空间的保双Lipschitz测度同胚，考虑其迭代的Lipschitz范数所构成的序列.我们得到下界的增长率的序列假设我们的同胚混合Lipschitz函数。特别地，我们得到了一个普适的下界，它依赖于空间的维数，但不依赖于混合率。此外，我们得到了快速混合情况下增长率的一个下界。后者被证明是尖锐的：相应的例子是由一个符号动力系统与鲁丁-夏皮罗序列。
英文摘要：
Given a bi-Lipschitz measure-preserving homeomorphism of a compact metric measure space of finite dimension, consider the sequence formed by the Lipschitz norms of its iterations. We obtain lower bounds on the growth rate of this sequence assuming that our homeomorphism mixes a Lipschitz function. In particular, we get a universal lower bound which depends on the dimension of the space but not on the rate of mixing. Furthermore, we get a lower bound on the growth rate in the case of rapid mixing. The latter turns out to be sharp: the corresponding example is given by a symbolic dynamical system associated to the Rudin-Shapiro sequence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
