Decay of correlations on Abelian covers of isometric extensions of Anosov flows

by Dr Sebastián Muñoz-Thon (Université Paris-Saclay)

Friday Jun 19, 2026, 2:15 PM → 3:05 PM Europe/Berlin

Endenicher Allee 60, Seminarraum 0.011 (Mathezentrum)

Abstract: 

I will report on a recent work with M. Cekić and T. Lefeuvre. We prove a complete asymptotic expansion of the correlation function in inverse powers of the time variable, for flows which arise as Abelian extensions, that is, extensions to $\mathbb{Z}^d$-covers, of certain partially hyperbolic flows. This includes the frame flow of an Abelian cover of a negatively curved closed Riemannian manifold $(M, g)$, if the frame flow on $(M, g)$ is ergodic. As a special case, our theorem also applies to Abelian extensions of Anosov flows. The proof uses Fourier series in $\mathbb{Z}^d$ (Floquet theory), (microlocal) anisotropic Sobolev spaces tailored to the dynamics, as well as the semiclassical Borel-Weil calculus on principal bundles.