Recent Results About Stable Ergodicity

By Keith Burns, C. Pugh, M. Shub, Amie Wilkinson. 2000

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MINIMALITY OF STRONG STABLE AND UNSTABLE FOLIATIONS FOR PARTIALLY HYPERBOLIC DIFFEOMORPHISMS (2002, background): “other (see, for example, the example in [28]), and many problems are common to both theories (see the survey [9] on stable ergodicity).”
A C^1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources (2003, background): “See [BPSW] for a survey on stable ergodicity and [DW] for recent progress on the previous conjecture.”
On mixing properties of compact group extensions of hyperbolic systems (2002, background): “nilpotent extensions, etc (see [15] for more discussion).”
Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents (2008, background): “See [8], [12], [13] and references therein for more information.”
Partial hyperbolicity for symplectic diffeomorphisms (2004, background): “We propose the reader to see [7] for approaches to prove stable ergodicity in the partially hyperbolic case.”
Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows (2011, background): “For a discussion of partial hyperbolicity, with examples and open questions, see [13, 40, 46].”