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1999/2000 Typical Continuous Functions Are Not Chaotic in the Sense of Devaney
Roy A. Mimna
Real Anal. Exchange 25(2): 947-954 (1999/2000).


We show that typical continuous functions of the form $f:M \to M$, where $M$ is a compact metric space with the fixed-point property and the absolute-retract property, are not chaotic in the sense of Devaney. Typical continuous functions on the compact interval have been shown to be chaotic in terms of other definitions of chaos. Results are also presented concerning the chain recurrent set for typical continuous functions and concerning functions for which the chain recurrent set is the entire space.


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Roy A. Mimna. "Typical Continuous Functions Are Not Chaotic in the Sense of Devaney." Real Anal. Exchange 25 (2) 947 - 954, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 3 January 2009

zbMATH: 1012.37010
MathSciNet: MR1778547

Primary: 26A18 , 54H20‎

Keywords: asymptotically stable set , Chain recurrent set , Devaney's chaos , sensitive dependence on initial conditions , transitivity , typical continuous functions

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 2 • 1999/2000
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