Twist systems on the interval

Volume 175 / 2002

Jozef Bobok Fundamenta Mathematicae 175 (2002), 97-117 MSC: 26A18, 37A05, 37E05, 37E45. DOI: 10.4064/fm175-2-1

Abstract

Let\/ $I$ 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.

Authors

  • Jozef BobokKM FSv. ČVUT
    Thákurova 7
    166 29 Praha 6, Czech Republic
    e-mail

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