- 99-424 Jos F. Alves, Marcelo Viana
- Statistical stability for robust classes of maps with non-uniform expansion
Nov 10, 99
(auto. generated ps),
of related papers
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.