Abstract
In the first part of this paper, for eachd≥2, we construct diffeomorphisms of thed-dimensional ball which have zero entropy, one periodic orbit with period 2n for eachn≥0, no other periodic orbits, and a single invariant Cantor set which has a continuum of possible but, in any case, simple geometric structures. These diffeomorphisms areC r(d)-smooth, wherer(d) is a strictly increasing function ofd, which goes to infinity withd. The second part contains a more general result about smooth maps obtained by an infinite sequence of surgeries, and further particular cases.
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