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

Marcelo Viana | Alves, José F.

Keywords: SRB measure | statistical stability | non-uniform hyperbolicity

We consider open sets of transformations in a manifold $M$, exhibiting non-uniformly expanding behaviour in some forward invariant domain $U\subset M$. Assuming that each transformation has a unique SRB measure in $U$, and some general uniformity conditions, we prove that the SRB measure varies continuously with the dynamics in the $L^1$-norm. As an application we show that an open class of maps introduced in \cite{V} fits this situation, thus proving that the SRB measures constructed in \cite{A} vary continuously with the map.

Anexos:

• av.ps