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

Yunping Jiang·David Ruelle
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Abstract

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.

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Yunping Jiang, David Ruelle. 2005-01-11. Analyticity of the Susceptibility Function for Unimodal Markovian Maps of the Interval. https://doi.org/10.1088/0951-7715%2F18%2F6%2F002

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