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Statistical stability for robust classes of maps with non-uniform expansion

Jose F. Alves·Marcelo Viana
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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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Jose F. Alves, Marcelo Viana. 2000-11-22. Statistical stability for robust classes of maps with non-uniform expansion. https://arxiv.org/abs/math/0011183

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