Definition of Symplectomorphisms. Meaning of Symplectomorphisms. Synonyms of Symplectomorphisms

- Hamiltonian mechanics follows. Symplectomorphisms that arise from Hamiltonian vector fields are known as Hamiltonian symplectomorphisms. Since {H, H} = XH(H) =...
- quantum cohomology. A version of the product also exists for non-exact symplectomorphisms. For the cotangent bundle of a manifold M, the Floer homology depends...
- generates a one-parameter family of symplectomorphisms and if {G, H} = 0, then G is conserved and the symplectomorphisms are symmetry transformations. A Hamiltonian...
- on a symplectic manifold can be given as a one-parameter family of symplectomorphisms (i.e., canonical transformations, area-preserving diffeomorphisms)...
- The Arnold conjecture on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian intersections was also a motivation in the development...
- by a smooth Hamiltonian over a symplectic manifold. The flows are symplectomorphisms and hence obey Liouville's theorem. This was soon generalized to flows...
- are known as canonical transformations in physics and (Hamiltonian) symplectomorphisms in mathematics. Hamiltonian vector fields can be defined more generally...
- functions. For symplectic manifolds, the transition functions must be symplectomorphisms. The structure on the manifold depends on the atlas, but sometimes...
- "Quantization problems suggest that the category of symplectic manifolds and symplectomorphisms be augmented by the inclusion of canonical relations as morphisms...
- with a differential structure, typically differentiable manifolds. A symplectomorphism is an isomorphism of symplectic manifolds. A permutation is an automorphism...