On periodic points of Hamiltonian diffeomorphisms of $\mathbb{C} \mathrm{P}^d$ via generating functions

Inspired by the techniques of Givental and Théret, we provide a proof with generating functions of a recent result of Ginzburg–Gürel concerning the periodic points of Hamiltonian diffeomorphisms of $\mathbb{C} \mathrm{P}^d$. For instance, we are able to prove that fixed points of pseudo-rotations are isolated as invariant sets or that a Hamiltonian diffeomorphism with a hyperbolic fixed point has infinitely many periodic points.

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Received 13 August 2020

Accepted 4 January 2021

Published 21 October 2022