Tower multiplexing and slow weak mixing

TL;DR

This paper introduces a method to combine ergodic transformations to analyze rigidity in weak mixing systems, showing that any rigidity sequence can be realized by a weakly mixing transformation.

Contribution

It presents a novel multiplexing technique to construct weak mixing transformations with prescribed rigidity sequences, advancing understanding of rigidity in dynamical systems.

Findings

Any rigidity sequence for an ergodic transformation can be realized by a weak mixing transformation.

The multiplexing technique enables the construction of weakly mixing systems with specific rigidity properties.

The work broadens the class of rigidity sequences known for weakly mixing systems.

Abstract

A technique is presented for multiplexing two ergodic measure preserving transformations together to derive a third limiting transformation. This technique is used to settle a question regarding rigidity of weak mixing transformations. Namely, given any rigidity sequence for an ergodic measure preserving transformation, there exists a weak mixing transformation which is rigid along the same sequence. This establishes a wide range of rigidity sequences for weakly mixing dynamical systems.