A rigorous computational approach to linear response*This work was mainly conducted during a visit of SG to Loughborough University. WB and SG would like to thank The Leverhulme Trust for supporting mutual research visits through the Network Grant IN-2014-021. SG thanks the Department of Mathematical Sciences at Loughborough University for hospitality. WB thanks Dipartimento di Matematica, Universita di Pisa. The research of SG and IN is partially supported by EU Marie-Curie IRSES 'Brazilian-European partnership in Dynamical Systems' (FP7-PEOPLE-2012-IRSES 318999 BREUDS). IN was partially supported by CNPq and FAPERJ. IN would like to thank the Department of Mathematics at Uppsala University and the support of the KAW grant 2013.0315. (12th February 2018) - Bahsoun, Wael; Galatolo, Stefano; Nisoli, Isaia; Niu, Xiaolong
Abstract: We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an algorithm to rigorously compute the linear response. We apply our results to expanding circle maps. In particular, we present examples where we compute, up to a pre-specified error in the L ∞ -norm, the response of expanding circle maps under stochastic and deterministic perturbations. Moreover, we present an example where we compute, up to a pre-specified error in the L 1 -norm, the response of the intermittent family at the boundary; i.e. when the unperturbed system is the doubling map.