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 ##IMG## [http://ej.iop.org/images/0951-7715/31/3/1073/nonaa9a88ieqn001.gif] {$L^{infty}$} -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.
A rigorous computational approach to linear response
Galatolo, Stefano;
2018-01-01
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 ##IMG## [http://ej.iop.org/images/0951-7715/31/3/1073/nonaa9a88ieqn001.gif] {$L^{infty}$} -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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
