Lots of attention and research activity has been devoted to partially
hyperbolic dynamical systems and their perturbations in the past few decades;
however, the main emphasis has been on features such as stable ergodicity and
accessibility rather than stronger statistical properties such as existence of
SRB measures and exponential decay of correlations.
In fact, these properties have been previously proved under some specific
conditions (e.g. Anosov flows, skew products) which, in particular, do not
persist under perturbations.
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