Irrational Twist Systems for Interval Maps

Jozef Bobok; Milan Kuchta

doi:rae/1212412847

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Home > Journals > Real Anal. Exchange > Volume 27 > Issue 2 > Article

2001/2002 Irrational Twist Systems for Interval Maps

Jozef Bobok, Milan Kuchta

Real Anal. Exchange 27(2): 441-456 (2001/2002).

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Abstract

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.