Institute for Mathematical Sciences
Weak Disks of Denjoy Minimal Sets.
Abstract: This paper investigates the existence of Denjoy minimal sets and, more generally, strictly ergodic sets in the dynamics of
iterated homeomorphisms. It is shown that for the full
two-shift, the collection of such invariant sets with the weak
topology contains topological balls of all finite dimensions.
One implication is an analogous result that holds for
diffeomorphisms with transverse homoclinic points. It is also
shown that the union of Denjoy minimal sets is dense in the
two-shift and that the set of unique probability measures
supported on these sets is weakly dense in the set of all
shift-invariant, Borel probability measures.
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