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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
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.
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