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On variants of Arnold conjecture. (English) Zbl 07285965
Summary: In this note we discuss the collection of statements known as Arnold conjecture for Hamiltonian diffeomorphisms of closed symplectic manifolds. We provide an overview of the homological, stable and strong versions of Arnold conjecture for non-degenerate Hamiltonian systems, a few versions of Arnold conjecture for possibly degenerate Hamiltonian systems, the degenerate version of Arnold conjecture for Hamiltonian homeomorphisms and Sandon’s version of Arnold conjecture for contactomorphisms.
MSC:
53D12 Lagrangian submanifolds; Maslov index
53D42 Symplectic field theory; contact homology
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