Entropy-expansive maps

Rufus Bowen
1972 Transactions of the American Mathematical Society  
Let /: X -> X be a uniformly continuous map of a metric space. / is called /(-expansive if there is an oO so that the set $>c(x) = {y : d(Jn(x),fn(y))^e for all näO) has zero topological entropy for each xe X. For Xcompact, the topological entropy of such an /is equal to its estimate using e: h(f) = h(f, e). If X is compact finite dimensional and y. an invariant Borel measure, then /V"(/) = A"(/, A) for any finite measurable partition A of X into sets of diameter at most e. A number of examples
more » ... are given. No diffeomorphism of a compact manifold is known to be not A-expansive.
doi:10.1090/s0002-9947-1972-0285689-x fatcat:66bwkludkzhnza6zo7qaz7dx5i