Analyticity of the Susceptibility Function for Unimodal Markovian Maps of the Interval

Details Analyticity of the Susceptibility Function for Unimodal Markovian Maps of the Interval Analyticity of the Susceptibility Function for Unimodal Markovian Maps of the Interval

2005-01-11

arxiv.org/abs/math/0501161v1

Mathematics

Dynamical Systems

8 pages

Scientific paper

10.1088/0951-7715/18/6/002

In a previous note [Ru] the susceptibility function was analyzed for some examples of maps of the interval. The purpose of the present note is to give a concise treatment of the general unimodal Markovian case (assuming $f$ real analytic). We hope that it will similarly be possible to analyze maps satisfying the Collet-Eckmann condition. Eventually, as explained in [Ru], application of a theorem of Whitney [Wh] should prove differentiability of the map $f\mapsto\rho_f$ restricted to a suitable set.

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