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arXiv · 2601.22626

Sequence entropy of rank one systems

Shigenori Takeda
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Abstract

We study the sequence entropy of rank one measure-preserving systems along subexponential sequences. We prove that the sequence entropy along a large class of sequences can be infinite using Ornstein's probabilistic constructions. Moreover, we show that sequence entropy necessarily vanishes for subexponential sequences if the growth of tower heights remains below certain growth rates, and obtain a flexibility result for polynomial sequences at this critical threshold.

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Shigenori Takeda. 2026-01-30. Sequence entropy of rank one systems. https://arxiv.org/abs/2601.22626

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