Hyperbolicity, irrationality exponents and the eta invariant
Differential Geometry
2022-06-30 v2 Analysis of PDEs
Dynamical Systems
Abstract
We consider the remainder term in the semiclassical limit formula for the eta invariant on a metric contact manifold, proving in general that it is controlled by volumes of recurrence sets of the Reeb flow. This particularly gives a logarithmic improvement of the remainder for Anosov Reeb flows, while for certain elliptic flows the improvement is in terms of irrationality measures of corresponding Floquet exponents.
Cite
@article{arxiv.2009.07549,
title = {Hyperbolicity, irrationality exponents and the eta invariant},
author = {Nikhil Savale},
journal= {arXiv preprint arXiv:2009.07549},
year = {2022}
}
Comments
Important referee correction regarding Ehrenfest time in version 2. To appear in CPDE