On the Hofer-Zehnder conjecture on weighted projective spaces

Abstract

We prove an extension of the homology version of the Hofer-Zehnder conjecture proved by Shelukhin to the weighted projective spaces which are symplectic orbifolds. In particular, we prove that if the number of fixed points counted with their isotropy order as multiplicity of a non-degenerate Hamiltonian diffeomorphism of such a space is larger than the minimum number possible, then there are infinitely many periodic points.

arXiv comment22 pages. arXiv admin note: text overlap with arXiv:2010.14172

References in corpus (6)

• Periodic points of Hamiltonian surface diffeomorphisms
• A symplectic proof of a theorem of Franks
• Quantitative Heegaard Floer cohomology and the Calabi invariant
• On the existence of infinitely many non-contractible periodic orbits of Hamiltonian diffeomorphisms of closed symplectic manifolds
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Cited by in corpus (2)

• Barcode entropy for Reeb flows on contact manifolds with Liouville fillings
• Invariant Sets and Hyperbolic Closed Reeb Orbits