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<p>The investigation of nilpotent structures aims to uncover the underlying nilpotent information in general dynamical systems, as well as the dynamical behaviors of the systems with respect to the nilpotent structures. These structures play crucial roles in ergodic theory and topological dynamics, and their applications across several fields of mathematics, including combinatorial number theory.</p><p>In this paper we will review the results related to the nilpotent structures, with a particular emphasis on topological nilpotent structures of ℤ-actions. Furthermore, we present applications and state open questions for future research.</p>

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Nilpotent Structures in Dynamical Systems

  • 期刊论文

  • 发表日期：

    2026年3月15日

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  • Wen Huang,
  • Jiahao Qiu,
  • Song Shao,
  • Xiangdong Ye

摘要

The investigation of nilpotent structures aims to uncover the underlying nilpotent information in general dynamical systems, as well as the dynamical behaviors of the systems with respect to the nilpotent structures. These structures play crucial roles in ergodic theory and topological dynamics, and their applications across several fields of mathematics, including combinatorial number theory.

In this paper we will review the results related to the nilpotent structures, with a particular emphasis on topological nilpotent structures of ℤ-actions. Furthermore, we present applications and state open questions for future research.