The long-term average response of observables of chaotic systems to dynamical
perturbations can often be predicted using linear response theory, but not all chaotic …

This theoretical work considers the following conundrum: linear response theory is
successfully used by scientists in numerous fields, but mathematicians have shown that …

Using a sensitive statistical test we determine whether or not one can detect the breakdown
of linear response given observations of deterministic dynamical systems. A goodness-of-fit …

In this paper, we study the differentiability of SRB measures for partially hyperbolic systems.
We show that for any s ≧ 1 s≥ 1, for any integer ℓ ≧ 2 ℓ≥ 2, any sufficiently large r, any φ …

We derive Edgeworth expansions that describe corrections to the Gaussian limiting
behaviour of slow–fast systems. The Edgeworth expansion is achieved using a semi-group …

Abstract For f_t (x)= tx^ 2 ft (x)= tx 2 the quadratic family, we define the fractional
susceptibility function Ψ^ Ω _ ϕ, t_0 (η, z) Ψ ϕ, t 0 Ω (η, z) of f_t ft, associated to a C^ 1 C 1 …

We show that the response, frozen and semifreddo fractional susceptibility functions of
certain real-analytic unimodal families, at Misiurewicz parameters and for fractional …

We show a general relation between fixed point stability of suitably perturbed transfer
operators and convergence to equilibrium (a notion which is strictly related to decay of …

Baladi and Smania proved in (2008 Nonlinearity 21 677–711; 2010 Ergod. Theory Dyn.
Syst. 30 1–20) the linear response of the SRB measures for a family of the piecewise …

We associate to a perturbation $(f_t) $ of a (stably mixing) piecewise expanding unimodal
map $ f_0 $ a two-variable fractional susceptibility function $\Psi_\phi (\eta, z) $, depending …