The Ruelle invariant and convexity in higher dimensions

I will explain how to construct the Ruelle invariant of a symplectic cocycle over an arbitrary measure preserving flow. I will provide examples and computations in the case of Hamiltonian flows and Reeb flows (in particular, for toric domains). As an application of this invariant, I will construct toric examples of dynamically convex domains that are not symplectomorphic to convex ones in any dimension.

This talk is based on joint works arXiv:2012.12869 and arXiv:2205.00935 with Oliver Edtmair.