There are no chaotic mappings with residual scrambled sets

Author:

Gedeon T.

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference8 articles.

1. Chaos almost everywhere

2. A Chaotic Function with a Scrambled Set of Positive Lebesgue Measure

3. [1] Bruckner A. M. and Hu Thakyin , “On scrambled sets for chaotic functions”, (Preprint 1985).

4. Chaotic Functions with Zero Topological Entropy

5. A characterization of chaos

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