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29 March 2024
 
  » arxiv » math.DS/0011183

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Statistical stability for robust classes of maps with non-uniform expansion
Jose F. Alves ; Marcelo Viana ;
Date 22 Nov 2000
Subject Dynamical Systems MSC-class: 37D25, 37D45 | math.DS
AbstractWe consider open sets of maps in a manifold $M$ exhibiting non-uniform expanding behaviour in some domain $Ssubset M$. 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.
Source arXiv, math.DS/0011183
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