Real Analysis Exchange

Irrational Twist Systems for Interval Maps

Jozef Bobok and Milan Kuchta

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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.

Article information

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

Dates
First available in Project Euclid: 2 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1212412847

Mathematical Reviews number (MathSciNet)
MR1922660

Zentralblatt MATH identifier
1096.37020

Subjects
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

Keywords
Interval map twist system invariant measure

Citation

Bobok, Jozef; Kuchta, Milan. Irrational Twist Systems for Interval Maps. Real Anal. Exchange 27 (2001), no. 2, 441--456. https://projecteuclid.org/euclid.rae/1212412847


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