A generalization of the line translation theorem

TL;DR

This paper extends the line translation theorem by replacing the measure-preserving condition with an intersection property, broadening its applicability in topological dynamics.

Contribution

It generalizes the existing line translation theorem using brick decomposition and operations on essential topological lines, removing the measure-preserving assumption.

Findings

The theorem now applies under the intersection property instead of measure preservation.

The method involves brick decomposition and topological line operations.

This broadens the scope of the original line translation theorem.

Abstract

Through the method of brick decomposition and the operations on essential topological lines, we generalize the line translation theorem of Beguin, Crovisier, Le Roux [BCL] in the case where the property of preserving a finite measure with total support is replaced by the intersection property.