Symplectomorphism

Canonical Quantization - Mathematical Quantization
... described by an element of a symplectic manifold with the time evolution given by the symplectomorphism generated by a Hamiltonian function over the symplectic manifold ... With respect to such a unitary representation, a symplectomorphism in the classical theory would now deform to a (metaplectic) unitary transformation ... In particular, the time evolution symplectomorphism generated by the classical Hamiltonian deforms to a unitary transformation generated by the corresponding quantum Hamiltonian ...

Symplectomorphism - Arnold Conjecture
... relates the minimum number of fixed points for a Hamiltonian symplectomorphism ƒ on M, in case M is a closed manifold, to Morse theory ...

Symplectic Floer Homology
... to a symplectic manifold and a nondegenerate symplectomorphism of it ... If the symplectomorphism is Hamiltonian, the homology arises from studying the symplectic action functional on the (universal cover of the) free loop space of a symplectic manifold ... invariant under Hamiltonian isotopy of the symplectomorphism ...