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Weak disks of Denjoy minimal sets

Published online by Cambridge University Press:  19 September 2008

Philip Boyland
Philip Boyland
Affiliation:
Institute for Mathematical Sciences, SUNY at Stony Brook, Stony Brook, NY 11794, USA
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Abstract

We investigate 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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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 4 , December 1993 , pp. 597 - 614
Copyright
Copyright © Cambridge University Press 1993

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