On scrambled sets for chaotic functions

Bruckner, A. M.; Hu, Thakyin

doi:10.1090/S0002-9947-1987-0879574-0

On scrambled sets for chaotic functions
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by A. M. Bruckner and Thakyin Hu

Trans. Amer. Math. Soc. 301 (1987), 289-297

DOI: https://doi.org/10.1090/S0002-9947-1987-0879574-0

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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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