Address: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18000 Praha 8, Czech Republic
E-mail: golovko@karlin.mff.cuni.cz
Abstract: 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.
AMSclassification: primary 53D12; secondary 53D42.
Keywords: Arnold conjecture, fixed points, Hamiltonian symplectomorphisms.
DOI: 10.5817/AM2020-5-277