Real Analysis Exchange

Irrational Twist Systems for Interval Maps

Jozef Bobok and Milan Kuchta

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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.

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Real Anal. Exchange, Volume 27, Number 2 (2001), 441-456.

First available in Project Euclid: 2 June 2008

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Zentralblatt MATH identifier

Primary: 26A18: Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25] 37A05: Measure-preserving transformations 37E05: Maps of the interval (piecewise continuous, continuous, smooth) 37E45: Rotation numbers and vectors

Interval map twist system invariant measure


Bobok, Jozef; Kuchta, Milan. Irrational Twist Systems for Interval Maps. Real Anal. Exchange 27 (2001), no. 2, 441--456.

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