Proof of the index conjecture in Hofer geometry

Let $\gamma$ be an Ustilovsky geodesic and $H$ its generating function. We give a simple proof of a generalization of the conjecture stated in [7], 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.

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Published 28 April 2014