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<p>We study multiple recurrence properties along separated cross sections for pmp actions of unimodular lcsc group on Polish spaces. We establish a multiple transverse recurrence theorem under the assumption that sufficiently large powers of the return time set are Delone sets. Typical examples of such situations arise from the theory of uniform approximate lattices.</p>

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Intersection spaces and multiple transverse recurrence

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月13日

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  • Michael Björklund,
  • Tobias Hartnick,
  • Yakov Karasik

摘要

We study multiple recurrence properties along separated cross sections for pmp actions of unimodular lcsc group on Polish spaces. We establish a multiple transverse recurrence theorem under the assumption that sufficiently large powers of the return time set are Delone sets. Typical examples of such situations arise from the theory of uniform approximate lattices.