Rigorous Computation of Linear Response for Intermittent Maps

Abstract

We present a rigorous numerical scheme for the approximation of the linear response of the invariant density of a map with an indifferent fixed point, with explicit and computed estimates for the error and all the involved constants.

Linear response for intermittent maps with critical point

“…Then, the main issue in repeating the steps in the proof of theorem 1.1 is that, for α > 0, the constant in (11) becomes large as α 0. However, similar to [10], this issue can be circumvented by writing (32). This decomposition together with the previously mentioned properties can be employed to derive the linear response formula.…”

“…The map T α,1 is uniformly expanding except at the neutral fixed point at the origin. In this case, robustness of statistical properties have been investigated for both deterministic [6,10,18,27,32,40] and random perturbations [5]. Independently, Baladi and Todd [10] and Korepanov [27] analyzed the regularity properties of the map R ϕ (α) := ´1 0 ϕ dµ α,1 for ϕ ∈ L q with q > 1 sufficiently large, employing different methods.…”