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INVARIANT MEASURES AND UNIFORM POSITIVE ENTROPY PROPERTY FOR INVERSE LIMITS

Helianfa

1999Acta Scientiarum Naturalium Universitatis SunyatseniMathematics被引 1

摘要

In this paper, the interconnection of some ergodic properties between a continuous selfmap and its inverse limit is studied. It has been proved that (1) their invariant Borel probability measures are identical up to homeomorphism and (2) they preserve uniform positive entropy property simuitaneously. As applications, it is also proved that the upper semi-continu-ous properties of their entropy maps are restricted each other, and the entropy map of the asymptotically h-expansive continuous map is upper semi-contlnuous, at the same time a continuous map having u, p.e. is topological weakmixing.

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