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

TL;DR

This paper proves a central limit theorem for the normalized Newton quotient of averages of Lipschitz observables with respect to SRB measures on transversal families of piecewise expanding unimodal maps, showing convergence to a normal distribution.

Contribution

It establishes a CLT for the modulus of continuity of averages of observables on a new class of dynamical systems, extending probabilistic limit theorems to these maps.

Findings

Normalized Newton quotient converges to a normal distribution.

The result applies to Lipschitz functions with non-vanishing variation.

Provides a probabilistic limit theorem for dynamical averages.

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.