Mathematical Research Letters
Volume 20 (2013)
Proof of the index conjecture in Hofer geometry
Pages: 981 – 984
Let $\gamma$ be an Ustilovsky geodesic and $H$ its generating function. We give a simple proof of a generalization of the conjecture stated in , relating the Morse index of $\gamma$, as a critical point of the Hofer length functional, with the Conley Zehnder index of the extremizers of $H$, considered as periodic orbits.