On the susceptibility function of piecewise expanding interval maps

Preprint

13 February 2007

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.*We propose a new version of Ruelle's conjectures.* In this revised version, we corrected a few minor mistakes and added Conjectures A and B and Remark 4.5.

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.

This publication has 0 references indexed in Scilit: