Proof of the index conjecture in Hofer geometry

Original · EN

Let γ be a non-degenerate Ustilovsky geodesic in Ham (M, ω) generated by H. We give a simple proof of a generalization of the conjecture stated in virtmorse, relating the Morse index of γ, as a critical point of the Hofer length functional, with the Conley Zehnder index of the extremizers of H, considered as periodic orbits.