Abstract

Let $I$ be a compact real interval and let $f:I->I$ be continuous. In our rather survey lecture we describe an interval analogy of the irrational circle rotation that occurs as a subsystem of the dynamical system $(I,f)$ - we call it an irrational twist system. Using a coding we show that any irrational twist system is strictly ergodic. We also prove that irrational twist systems exist as subsystems of a large class of systems $(I,f)$ having a cycle of odd period greater than one.