Stably ergodic approximation: two examples

Authors
Shub, M Wilkinson, A
Citation
M. Shub et A. Wilkinson, Stably ergodic approximation: two examples, ERGOD TH DY, 20, 2000, pp. 875-893
Citations number
11
Categorie Soggetti
Mathematics
Journal title
ERGODIC THEORY AND DYNAMICAL SYSTEMS
ISSN journal
01433857 → ACNP
Volume
20
Year of publication
2000
Part
3
Pages
875 - 893
Database
ISI
SICI code
0143-3857(200006)20:<875:SEATE>2.0.ZU;2-V
Abstract
It has been conjectured that the stably ergodic diffeomorphisms are open an d dense in the space of volume-preserving, partially hyperbolic diffeomorph isms of a compact manifold. In this paper we deal with two recalcitrant exa mples, 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 ergod ic diffeomorphisms which have the stable accessibility property.