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

Abstract

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 $\mathbb{C}{\text{P}}^d$. 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.

31 pages

References in corpus (2)

• Functors and Computations in Floer homology with Applications Part II
• On the Hofer-Zehnder conjecture

Cited by in corpus (4)

• On the Hofer-Zehnder conjecture on $\mathbb{C}{\text{P}}^d$ via generating functions (with an appendix by Egor Shelukhin)
• On the Barcode Entropy of Reeb Flows
• On the Hofer-Zehnder conjecture on weighted projective spaces
• Invariant Sets and Hyperbolic Closed Reeb Orbits