99-424 Jos F. Alves, Marcelo Viana
Statistical stability for robust classes of maps with non-uniform expansion (411K, postscript) Nov 10, 99
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Abstract. We consider open sets of maps in a manifold \$M\$ exhibiting non-uniform expanding behaviour in some domain \$S\subset 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 \$L^1\$-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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