A rank one mild mixing system without minimal self joinings

Key Points

• This research aims to identify a rank one transformation exhibiting mild mixing properties while lacking minimal self-joinings.
• Develop a mathematical framework for analyzing rank one transformations.
• Explore properties of mildly mixing systems and their relationship to self-joinings.
• Demonstrated the existence of a rank one transformation with mild mixing properties.
• Confirmed that this transformation does not possess minimal self-joinings, providing a novel example in the field.