Hyperbolicity, irrationality exponents and the eta invariant

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.

Important referee correction regarding Ehrenfest time in version 2. To appear in CPDE

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