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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On scrambled sets for chaotic functions


Authors: A. M. Bruckner and Thakyin Hu
Journal: Trans. Amer. Math. Soc. 301 (1987), 289-297
MSC: Primary 26A18; Secondary 54H20, 58F13
MathSciNet review: 879574
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Abstract: Some recent research has raised questions concerning the possible sizes of scrambled sets for chaotic functions. We answer these questions by showing that a scrambled set can have full measure, but cannot be residual although a scrambled set can be second category in every interval. We also indicate relationships that exist between chaotic functions and transitive functions.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0879574-0
Keywords: Chaotic functions, scrambled sets, transitive (or nomadic) functions
Article copyright: © Copyright 1987 American Mathematical Society