Title: Rigid-Recurrent Sequences for Actions of Finite Exponent Groups Show Chinese title

Title: 有限指数群作用的刚性递归序列

Abstract: The focus of this paper is to better understand the coexistence of rigidity, weak mixing, and recurrence by constructing thin sets in the product of countably many copies of the finite cyclic group of order q. A Kronecker-type set K is a subset of this group on which every continuous function into the complex unit circle equals the restriction, to K, of a character in the group's Pontryagin dual. Ackelsberg proves that if, for all q > 1, there exists a perfect Kronecker-type set generating a dense subgroup, then there exist large rigidity sequences for weak mixing systems of actions by countable discrete abelian groups. Ackelsberg shows the existence of such sets for prime values of q, while we construct them for all q > 1. Show Chinese abstract

Abstract: 本文的重点在于通过构造可数多个有限循环群的乘积中的稀疏集，更好地理解刚性、弱混合和回复之间的共存关系。 一个Kronecker型集 \( K \) 是该群的一个子集，在此子集上，每个连续函数到复单位圆都等于该群Pontryagin对偶中某个特征函数在此子集上的限制。 Ackelsberg证明了，如果对于所有 \( q > 1 \)，存在生成稠密子群的完美Kronecker型集，则存在计数离散阿贝尔群作用下弱混合系统的大量刚性序列。 Ackelsberg展示了当 \( q \) 为素数值时此类集的存在性，而我们则构造出所有 \( q > 1 \) 的情况下的此类集。