Resonant spaces for volume preserving Anosov flows

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• Gabriel Paternain, Cambridge
• Wednesday 05 February 2020, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

Recently Dyatlov and Zworski proved that the order of vanishing of the Ruelle zeta function at zero, for the geodesic flow of a negatively curved surface, is equal to minus the Euler characteristic of the surface. They more generally considered contact Anosov flows on 3-manifolds. In this talk, I will discuss how this result needs to be modified to include all volume-preserving Anosov flows. Several new features will appear, like the winding cycle and the helicity of the flow. A key question is the (non-)existence of Jordan blocks for one forms (semi-simplicity) and I will discuss examples where Jordan blocks do appear, as well as describe a resonance splitting phenomenon near contact flows when we deform with non-zero winding cycle. This is joint work with Mihajlo Cekic.

This talk is part of the Differential Geometry and Topology Seminar series.

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