Preprint A39/2007
On the susceptibility function of piecewise expanding interval maps

DDIC

**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.