The Arnold conjecture relates the number of fixed points of a Hamiltonian diffeomorphism of
a closed symplectic manifold to the minimum
number of critical points of a smooth real
function. Its formulation using the ordinary Morse
number imposes nondegeneracy of every fixed point
and predicts at least 
fixed points. The formulation allowing degenerate fixed points predicts at least 
, the critical point
number. The bound using the stable Morse number
is another proposed refinement. These assertions are distinct from lower bounds expressed
only in terms of homology.
Arnold Conjecture
See also
Critical Point Number, Cup Length, Hamiltonian Diffeomorphism, Morse Number, Stable Morse Number, Symplectic ManifoldExplore with Wolfram|Alpha
References
Cannas da Silva, A. Lectures on Symplectic Geometry. Berlin: Springer-Verlag, 2001. https://people.math.ethz.ch/~acannas/Papers/lsg.pdf.Cite this as:
Weisstein, Eric W. "Arnold Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ArnoldConjecture.html