Central limit theorem for the modulus of continuity of averages of observables on transversal families of piecewise expanding unimodal maps

Abstract

We prove that the Newton quotient of the average R(t) of a lipschitzian function (with non vanishing variation) with respect to the SRB measure on a transversal family f_t of piecewise expanding unimodal maps, after an appropriated normalization, converges in distribution to the normal distribution.

References in corpus (3)

• On the susceptibility function of piecewise expanding interval maps
• Continuity properties of transport coefficients in simple maps
• Regularity of absolutely continuous invariant measures for piecewise expanding unimodal maps

Cited by in corpus (8)

• Linear response for macroscopic observables in high-dimensional systems
• On spurious detection of linear response and misuse of the fluctuation-dissipation theorem in finite time series
• On the smooth dependence of SRB measures for partially hyperbolic systems
• Edgeworth expansions for slow-fast systems with finite time scale separation
• Fractional susceptibility functions for the quadratic family: Misiurewicz-Thurston parameters
• On the fractional susceptibility function of piecewise expanding maps
• Pre-threshold fractional susceptibility functions at Misiurewicz parameters
• A parameter ASIP for the quadratic family