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arXiv · 1904.03424

Emergence via non-existence of averages

Shin Kiriki·Yushi Nakano·Teruhiko Soma
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Abstract

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.

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Shin Kiriki, Yushi Nakano, Teruhiko Soma. 2019-04-06. Emergence via non-existence of averages. https://doi.org/10.1016/j.aim.2022.108254

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