Real Analysis Exchange

Intervals Containing All the Periodic Points

M. Archana and V. Kannan

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Abstract

For any map $f$ from $\mathbb{R}$ to $\mathbb{R}$, if an interval $J$ contains all periodic points of period 1 and 2, then $f(f(J))$ contains all periodic points (and therefore contains the centre of $f$).

Article information

Source
Real Anal. Exchange, Volume 41, Number 2 (2016), 263-270.

Dates
First available in Project Euclid: 30 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rae/1490839329

Mathematical Reviews number (MathSciNet)
MR3597319

Zentralblatt MATH identifier
06848927

Subjects
Primary: 54C30: Real-valued functions [See also 26-XX] 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
Secondary: 37C25: Fixed points, periodic points, fixed-point index theory

Keywords
Periodic points period convex hull

Citation

Archana, M.; Kannan, V. Intervals Containing All the Periodic Points. Real Anal. Exchange 41 (2016), no. 2, 263--270. https://projecteuclid.org/euclid.rae/1490839329


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