Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Mihajlo Cekic
Affiliation:

Université Paris-Sud/MPIM
Date:

Thu, 21/11/2019 - 13:00 - 14:00 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 the negative Euler characteristic. They more generally considered contact Anosov flows on 3-manifolds. In this talk, I will discuss an extension of this result to volume-preserving Anosov flows, where new features appear: the winding cycle and the helicity of a vector field. A key question is the (non-)existence of Jordan blocks for one forms and I will give an example where Jordan blocks do appear, as well as describe a resonance splitting phenomenon near contact flows. This is joint work with Gabriel Paternain.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/3050