July  1996, 2(3): 349-350. doi: 10.3934/dcds.1996.2.349

Stably ergodic skew products

1. 

IBM Research, Watson Research Center, PO Box 218, Yorktown Heights, New York 10598

Received  October 1995 Published  May 1996

In [PS] it is conjectured that among the volume preserving $C^2$ diffeomorphisms of a closed manifold which have some hyperbolicity, the ergodic ones contain an open and dense set. In this paper we prove an analogous statement for skew products of Anosov diffeomorphisms of tori and circle rotations. Thus this paper may be seen as an example of the phenomenon conjectured in [PS]. The corresponding theorem for skew products of Anosov diffeomorphisms and translations of arbitrary compact groups is an interesting open problem.
Citation: Roy Adler, Bruce Kitchens, Michael Shub. Stably ergodic skew products. Discrete and Continuous Dynamical Systems, 1996, 2 (3) : 349-350. doi: 10.3934/dcds.1996.2.349
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