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ON THE EVENTUAL PERIODICITY OF PIECEWISE LINEAR CHAOTIC MAPS

Part of: Mathematical economics Topological dynamics Difference and functional equations, recurrence relations

Published online by Cambridge University Press:  16 February 2017

M. ALI KHAN  and
ASHVIN V. RAJAN
M. ALI KHAN*
Affiliation:
Department of Economics, Johns Hopkins University, Baltimore, MD 21218, USA email akhan@jhu.edu
ASHVIN V. RAJAN
Affiliation:
3935 Cloverhill Road, Baltimore, MD 21218, USA email ashvinrj@aol.com
*
✉akhan@jhu.edu
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Abstract

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We present a family of continuous piecewise linear maps of the unit interval into itself that are all chaotic in the sense of Li and Yorke [‘Period three implies chaos’, Amer. Math. Monthly82 (1975), 985–992] and for which almost every point (in the sense of Lebesgue) in the unit interval is an eventually periodic point of period $p,p\geq 3$, for a member of the family.

Keywords

Li–Yorke chaospiecewise linear functionseventual convergencealmost everywhere convergencedynamical systemsrationalisability

MSC classification

Primary: 37B20: Notions of recurrence
Secondary: 65Q10: Difference equations 91B55: Economic dynamics
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 3 , June 2017 , pp. 467 - 475
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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