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On the Hofer–Zehnder conjecture on weighted projective spaces

Part of: Variational problems in infinite-dimensional spaces Symplectic geometry, contact geometry Hamiltonian and Lagrangian mechanics

Published online by Cambridge University Press:  23 January 2023

Simon Allais
Simon Allais*
Affiliation:
Université de Paris, IMJ-PRG, 8 place Aurélie de Nemours, 75013 Paris, France [email protected]
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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.

Keywords

generating functionsHamiltonianperiodic pointssymplectic orbifoldweighted projective spaceHofer–Zehnder conjecturebarcodespersistence modules

MSC classification

Secondary: 70H12: Periodic and almost periodic solutions 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.) 53D20: Momentum maps; symplectic reduction
Type
Research Article
Information
Compositio Mathematica , Volume 159 , Issue 1 , January 2023 , pp. 87 - 108
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Copyright
© 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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