Twist systems on the interval
Volume 175 / 2002
Fundamenta Mathematicae 175 (2002), 97-117
MSC: 26A18, 37A05, 37E05, 37E45.
DOI: 10.4064/fm175-2-1
Abstract
Let\/ be a compact real interval and let f:I\rightarrow I be continuous. 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.