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Stably ergodic approximation: two examples

Published online by Cambridge University Press:  01 June 2000

MICHAEL SHUB  and
AMIE WILKINSON
MICHAEL SHUB
Affiliation:
IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA (e-mail: [email protected]) Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, USA (e-mail: [email protected])
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Abstract

It has been conjectured that the stably ergodic diffeomorphisms are open and dense in the space of volume-preserving, partially hyperbolic diffeomorphisms of a compact manifold. In this paper we deal with two recalcitrant examples; the standard map cross Anosov and the ergodic automorphisms of the 4-torus. In both cases we show that they may be approximated by stably ergodic diffeomorphisms which have the stable accessibility property.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 3 , June 2000 , pp. 875 - 893
Copyright
2000 Cambridge University Press

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