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arXiv · 2111.08360

High pointwise emergence and Katok's conjecture for systems with non-uniform structure

Yong Ji·Ercai Chen·Zijie Lin
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Abstract

Recently, Kiriki, Nakano and Soma introduced a concept called pointwise emergence as a new quantitative perspective into the study of non-existence of averages for dynamical systems. In the present paper, we consider the set of points with high pointwise emergence for systems with non-uniform structure and prove that this set carries full topological pressure. For the proof of this result, we show that such systems have ergodic measures of arbitrary intermediate pressures.

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Yong Ji, Ercai Chen, Zijie Lin. 2021-11-16. High pointwise emergence and Katok's conjecture for systems with non-uniform structure. https://doi.org/10.1088/1361-6544/ac8a3a

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