On scrambled sets for chaotic functions

@inproceedings{Bruckner1987OnSS,
  title={On scrambled sets for chaotic functions},
  author={Andrew Michael Bruckner and Thakyin Hu},
  year={1987}
}
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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