Simple mixing actions with uncountably many prime factors

TL;DR

This paper constructs a specific type of mixing transformation with uncountably many prime factors using (C,F)-construction, advancing understanding of complex dynamical systems with prime factor structures.

Contribution

It introduces a novel (C,F)-construction method to produce a 2-fold simple mixing transformation with uncountably many prime factors, a new example in ergodic theory.

Findings

Constructed a 2-fold simple mixing transformation with uncountably many prime factors.

Demonstrated all factors are non-trivial and proper.

Extended the class of known transformations with complex prime factor structures.

Abstract

Via (C,F)-construction we produce a 2-fold simple mixing transformation which has uncountably many non-trivial proper factors and all of them are prime.