Entropy-expansive maps
Author:
Rufus Bowen
Journal:
Trans. Amer. Math. Soc. 164 (1972), 323-331
MSC:
Primary 28.70; Secondary 54.00
DOI:
https://doi.org/10.1090/S0002-9947-1972-0285689-X
MathSciNet review:
0285689
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a uniformly continuous map of a metric space. f is called h-expansive if there is an
so that the set
for all
} has zero topological entropy for each
. For X compact, the topological entropy of such an f is equal to its estimate using
. If X is compact finite dimensional and
an invariant Borel measure, then
for any finite measurable partition A of X into sets of diameter at most
. A number of examples are given. No diffeomorphism of a compact manifold is known to be not h-expansive.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1972-0285689-X
Keywords:
Entropy,
h-expansive
Article copyright:
© Copyright 1972
American Mathematical Society