Analyticity of the SRB measure for holomorphic families of quadratic-like Collet-Eckmann maps

Baladi, Viviane; Smania, Daniel

doi:10.1090/S0002-9939-08-09651-2

Analyticity of the SRB measure for holomorphic families of quadratic-like Collet-Eckmann maps
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by Viviane Baladi and Daniel Smania PDF

Proc. Amer. Math. Soc. 137 (2009), 1431-1437 Request permission

Abstract:

We show that if $f_t$ is a holomorphic family of quadratic-like maps with all periodic orbits repelling so that for each real $t$ the map $f_t$ is a real Collet-Eckmann $S$-unimodal map, then, writing $\mu _t$ for the unique absolutely continuous invariant probability measure of $f_t$, the map \[ t\mapsto \int \psi d\mu _t \] is real analytic for any real analytic function $\psi$.

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