arXiv subjects

Amanda de Lima

Publications and source records attributed to Amanda de Lima.

3 recordsLinked to original sources

arXiv2018

Central limit theorem for generalized Weierstrass functions

Let $f$ be a $C^{2+ε}$ expanding map of the circle and $v$ be a $C^{1+ε}$ real function of the circle. Consider the twisted cohomological equation $v(x) = α(f(x)) - Df(x) α(x)$ which has a unique bounded solution $α$. We prove that $α$ is either $C^{1+ε}$ or nowhere differentiable, and if $α$ is nowhere differentiable then the Newton quotients of $α$, after an appropriated normalization, converges in distribution to the normal distribution, with respect to the unique absolutely continuous invariant probability of $f$.

math.DS↗

arXiv2016

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

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.

math.DS↗

arXiv2011

On infinitely cohomologous to zero observables

We show that for a large class of piecewise expanding maps T, the bounded p-variation observables u_0 that admits an infinite sequence of bounded p-variation observables u_i satisfying u_i(x)= u_{i+1}(Tx) -u_{i+1}(x) are constant. The method of the proof consists in to find a suitable Hilbert basis for L^2(hm), where hm is the unique absolutely continuous invariant probability of T. In terms of this basis, the action of the Perron-Frobenious and the Koopan operator on L^2(hm) can be easily understood. This result generalizes earlier results by Bamon, Kiwi, Rivera-Letelier and Urzua in the case T(x)= n x mod 1, n in N-{0,1} and Lipchitizian observables u_0.

math.DS↗