Emergence via non-existence of averages
Emergence via non-existence of averages
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DOI：
10.1016/j.aim.2022.108254
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发表时间：
2019-04
期刊：
影响因子：
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通讯作者：
Shin Kiriki;Yushi Nakano;Teruhiko Soma
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文献类型：
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作者：
Shin Kiriki;Yushi Nakano;Teruhiko Soma
受Berger最近工作的启发，我们引入了逐点涌现的概念。这个概念提供了一个新的定量的角度来研究不存在的平均动力系统。我们发现，高点态出现在一个大的集合上出现丰富的动力系统：任何连续映射在一个紧凑的度量空间的规格属性有超多项式点态出现在状态空间的剩余子集。进一步地，存在任意纽豪斯开集的稠密子集，其中每个元素在状态空间的正Lebesgue测度子集上具有超多项式逐点涌现。
Inspired by a recent work by Berger, we introduce the concept of pointwise emergence. This concept provides with a new quantitative perspective into the study of non-existence of averages for dynamical systems. We show that high pointwise emergence on a large set appears for abundant dynamical systems: Any continuous maps on a compact metric space with the specification property have super-polynomial pointwise emergence on a residual subset of the state space. Furthermore, there is a dense subset of any Newhouse open set each element of which has super-polynomial pointwise emergence on a positive Lebesgue measure subset of the state space.