Let $I$ be a compact real interval and $f\colon ~I\rightarrow I$ continuous. We describe a special infinite minimal subsystem - we call it irrational twist system - of dynamical system $(I,f)$. We show that any twist system has an extremely regular behavior and it can be considered as an interval analogy of the irrational circle rotation.
"Irrational Twist Systems for Interval Maps." Real Anal. Exchange 27 (2) 441 - 456, 2001/2002.