-
Hamiltonian mechanics follows.
Symplectomorphisms that
arise from
Hamiltonian vector fields are
known as
Hamiltonian symplectomorphisms.
Since {H, H} = XH(H) =...
- are
known as
canonical transformations in
physics and (Hamiltonian)
symplectomorphisms in mathematics.
Hamiltonian vector fields can be
defined more generally...
- 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...
-
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...
- by a
smooth Hamiltonian over a
symplectic manifold. The
flows are
symplectomorphisms and
hence obey Liouville's theorem. This was soon
generalized to flows...
-
generates a one-parameter
family of
symplectomorphisms and if {G, H} = 0, then G is
conserved and the
symplectomorphisms are
symmetry transformations. A Hamiltonian...
- with a
differential structure,
typically differentiable manifolds. A
symplectomorphism is an
isomorphism of
symplectic manifolds. A
permutation is an automorphism...
- form is a
canonical transformation;
these are a
special case of a
symplectomorphism,
which are
essentially a
change of
coordinates on a
symplectic manifold...
- (plégma), πλοκή (plokḗ), πλόκος plectics, plexogenic, ploce, symplectic,
symplectomorphism,
symploce plect-, plex-
plait Latin plectere,
plexus perplex pleg-...
