Analyticity of Riemannian exponential maps on ${\rm Diff}(\T)$

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

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 $f\mapstoρ_f$ restricted to a suitable set.