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

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

2008-01-22

arxiv.org/abs/0801.3356v1

Mathematics

Dynamical Systems

7 pages

Scientific paper

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 m_t for the unique absolutely
continuous invariant probability measure of f_t, the map t -> \int g dm_t is
real analytic for any real analytic function g.

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