English

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.

Keywords

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

R2 v1 2026-06-23T18:34:47.614Z