高校应用数学学报
高校應用數學學報
고교응용수학학보
APPLIED MATHEMATICS
1999年
3期
265-272
,共8页
Continuous map%inverse limit%invariant measure%entropy map%uniform positive entropy
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 simultaneously. As applications, it is also proved that the upper semi-continuous properties of their entropy maps are restricted each other, and the entropy map of the asymptotically h-expansive continuous map is upper semi-continuous, at the same time a continuous map having u.p.e. is topological weak-mixing.
