PARAMETER REGULARITY OF DYNAMICAL DETERMINANTS OF EXPANDING MAPS OF THE CIRCLE AND AN APPLICATION TO LINEAR RESPONSE

摘要

In order to adapt to the differentiable setting a formula for linear response proved by Pollicott and Vytnova in the analytic setting, we show a result of parameter regularity of dynamical determinants of expanding maps of the circle. Linear response can then be expressed in terms of periodic points of the perturbed dynamics.