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1995/1996 Register shifts versus transitive f-cycles for piecewise monotone maps
Jozef Bobok, Milan Kuchta
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Real Anal. Exchange 21(1): 134-146 (1995/1996).


This paper investigates the family of continuous piecewise monotone functions which map a closed interval of the real line into itself. For these maps Preston \cite{1} and Blokh \cite{2} described the asymptotic behavior of the orbit of a “typical” point. Our results show that if the map is expanding on its intervals of monotonicity the dominant role is played by transitive \(f\)-cycles. Contrary to this for a “typical” map in a natural closure of the space of these maps there are no transitive \(f\)-cycles. Instead the behavior is dominated by the register shifts. This result is illustrated by an example.


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Jozef Bobok. Milan Kuchta. "Register shifts versus transitive f-cycles for piecewise monotone maps." Real Anal. Exchange 21 (1) 134 - 146, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 3 July 2012

zbMATH: 0849.26002
MathSciNet: MR1377523

Primary: 26A18 , 26A21 , 54H20‎ , 58F08

Keywords: asymptotic behavior , expanding maps , iteration , Piecewise monotone , Register shift , Residual set , Transitive \(f\)-cycle

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 1 • 1995/1996
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