MATHEMATICA BOHEMICA, Vol. 120, No. 3, pp. 293-298, 1995

A characterization of chaotic functions with entropy zero via their maximal scrambled sets

Francisco Balibrea, Victor Jimenez Lopez

Departamento de Matematicas, Universidad de Murcia, Campus de Espinardo, Aptdo. de Correos 4021, 30100 Murcia, Spain, e-mail: balibrea@fcu.um.es, vjimenez@fcu.um.es

Abstract: In this note we characterize chaotic functions (in the sense of Li and Yorke) with topological entropy zero in terms of the structure of their maximal scrambled sets. In the interim a description of all maximal scrambled sets of these functions is also found.

Keywords: chaotic functions, scrambled sets

Classification (MSC91): 58F13, 26A18, 54H20

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