Bulletin of the Australian Mathematical Society

Research Article

There are no chaotic mappings with residual scrambled sets

T. Gedeona1

a1 Katedra algebry, Faculty of Mathematics and Physics, Komensky University, 842 15 Bratislava, Czecholovakia.

A continuous mapping f of a compact real interval I to itself which is chaotic in the sense of Li and Yorke, cannot have a scrambled set residual in an subinterval of I. This shows that chaos in this case cannot be large from a topological point of view.

(Received November 17 1986)