249 research outputs found
Uniformly Positive Entropy of Induced Transformations
Let be a topological dynamical system consisting of a compact metric
space and a continuous surjective map . By using local entropy
theory, we prove that has uniformly positive entropy if and only if so
does the induced system (\cM(X),\wt{T}) on the space of Borel probability
measures endowed with the weak topology. This result can be seen as a
version for the notion of uniformly positive entropy of the corresponding
result for topological entropy due to Glasner and Weiss.Comment: To apper in ETD
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