On the susceptibility function of piecewise expanding interval maps

Preprint

29 December 2006

preprint
Published by arXiv in arXiv

Abstract

We study the susceptibility function Psi(z) associated to the perturbation f_t=f+tX of a piecewise expanding interval map f. 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 of f_t with respect to t, we present examples satisfying our conditions so that the SRB measure is not Lipschitz.

Keywords

PIECEWISE EXPANDING INTERVAL
SUSCEPTIBILITY FUNCTION
EXPANDING INTERVAL MAP
INTERVAL MAP
SRB MEASURE
F_T
PSI

All Related Versions

Version 1, 2006-12-29, ArXiv
Version 2, 2007-02-13, ArXiv
Version 3, 2007-03-11, ArXiv
Published version: Communications in Mathematical Physics, 275 (3), 839.

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