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A transformation on a symplectic manifold that preserves the symplectic form and hence the structure of the manifold.

A method for integrating dynamical systems that relies on the Lie series expansion and reordering of operator exponentials.

A smooth manifold equipped with a closed non-degenerate differential 2-form known as the symplectic form.

A dynamical system governed by Hamilton's equations, expressed in terms of coordinates and conjugate momenta.

A symplectic integrator method that updates positions and momenta in a staggered fashion.

A numerical method for solving Newton's equations of motion that is symplectic and time-reversible.

A measure of the directional derivative of one function along the Hamiltonian flow of another function within Hamiltonian dynamics.

A change of coordinates in phase space that preserves the form of Hamilton's equations and is defined by a generating function.

A numerical method used to integrate Hamiltonian systems that preserves the symplectic structure of phase space.