Hamiltonian Vector field: Symplectic manifold, Diffeomorphism, Canonical transformation, Symplectomorphism, Lie bracket, Differentiable function, field

Energy Drift: Verlet Integration, Hamiltonian Mechanics, Symplectic Integrator

Quasi Invariant Measure: Measure Space, Numerical Function, Smooth Manifold, Diffeomorphism, Lebesgue Measure, Euclidean Theory

Projective Connection: Differential Geometry, Cartan Connection, Differentiable Manifold

Riemannian Manifold: Differentiable Manifold, Tangent Space, Inner Product Positive Definite, Symmetric Tensor, Metric Tensor