Statistical stability for robust classes of maps with non-uniform expansion
نویسندگان
چکیده
We consider open sets of maps in a manifold M exhibiting non-uniform expanding behaviour in some domain S ⊂ M . Assuming that there is a forward invariant region containing S where each map has a unique SRB measure, we prove that under general uniformity conditions, the SRB measure varies continuously in the L1-norm with the map. As a main application we show that the open class of maps introduced in [V] fits to this situation, thus proving that the SRB measures constructed in [A] vary continuously with the map.
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