Area expanding C^{1+\alpha} Suspension Semiflows
Dynamical Systems
2015-06-11 v2
Abstract
We study a large class of suspension semiflows which contains the Lorenz semiflows. This is a class with low regularity (merely C^{1+\alpha}) and where the return map is discontinuous and the return time is unbounded. We establish the functional analytic framework which is typically employed to study rates of mixing. The Laplace transform of the correlation function is shown to admit a meromorphic extension to a strip about he imaginary axis. As part of this argument we give a new result concerning the quasi-compactness of weighted transfer operators for piecewise C^{1+\alpha} expanding interval maps.
Cite
@article{arxiv.1210.3291,
title = {Area expanding C^{1+\alpha} Suspension Semiflows},
author = {Oliver Butterley},
journal= {arXiv preprint arXiv:1210.3291},
year = {2015}
}