Preprint A39/2007
On the susceptibility function of piecewise expanding interval maps
Viviane Baladi
Keywords: SRB measure | susceptibility function | interval map
We study the susceptibility function Psi(z) associated to the perturbation of a piecewise expanding interval map. The analysis is based on a spectral description of transfer operators. It gives in particular sufficient conditions which guarantee that \Psi(z) is holomorphic in a disc of larger than one. Although \Psi(1) is the formal derivative of the SRB measure we present examples satisfying our conditions so that the SRB measure is not Lipschitz.