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

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 $f\mapsto {\rho }_f$ restricted to a suitable set.

8 pages

References in corpus (1)

• Differentiating the absolutely continuous invariant measure of an interval map f with respect to f

Cited by in corpus (11)

• A review of linear response theory for general differentiable dynamical systems
• On the susceptibility function of piecewise expanding interval maps
• Linear response in neuronal networks: from neurons dynamics to collective response
• Does the complex susceptibility of the Henon map have a pole in the upper-half plane ? A numerical investigation
• Continuity properties of transport coefficients in simple maps
• Fractional susceptibility functions for the quadratic family: Misiurewicz-Thurston parameters
• Singularities of the susceptibility of an SRB measure in the presence of stable-unstable tangencies
• On the fractional susceptibility function of piecewise expanding maps
• Teichmüller Structures and Dual Geometric Gibbs Type Measure Theory for Continuous Potentials
• Function Models for Teichmüller Spaces and Dual Geometric Gibbs Type Measure Theory for Circle Dynamics
• Pre-threshold fractional susceptibility functions at Misiurewicz parameters