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In page Symplectomorphism:

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A celebrated conjecture of Vladimir Arnold relates the minimum number of fixed points for a Hamiltonian symplectomorphism f on M, in case M is a closed manifold, to Morse theory. More precisely, the conjecture states that f has at least as many fixed points as the number of critical points that a smooth function on M must have (understood as for a generic case, Morse functions, for which this is a definite finite number which is at least 2).[1]