| Stably Ergodic Approximation: Two Examples (2000) | |||||||||||||||
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 four torus. In both cases we show that they may be approximated by stably ergodic diffeomorphisms which have the stable accessibility property. Introduction It has been conjectured in [PS2] that the stably ergodic diffeomorphisms are open and dense in the space of volume-preserving, partially hyperbolic diffeomorphisms of a compact manifold. Recall that a diffeomorphism f : M !M of a compact manifold M is partially hyperbolic if the tangent bundle TM splits as a Whitney sum of Tf-invariant subbundles: TM = E u \Phi E c \Phi E s ; and there exist a Riemannian (or Finsler) metric on M and constants ! 1 and ? 1 such that for every p 2 M , m(T p f j E u) ? ? kT p f j E ck m(T p f j E... | |||||||||||||||
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