On infinitely cohomologous to zero observables
Abstract
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.
Cite
@article{arxiv.0907.5013,
title = {On infinitely cohomologous to zero observables},
author = {Amanda de Lima and Daniel Smania},
journal= {arXiv preprint arXiv:0907.5013},
year = {2018}
}
Comments
24 pages. We included new results by A. Avila. He kindly agreed to include them in this new version. We also fixed some typos