On scrambled sets for chaotic functions
Andrew M. Bruckner, Thakyin Hu · Transactions of the American Mathematical Society · 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.