Hamiltonian minimality and Hamiltonian stability of Gauss maps

Surface terms and the Gauss-Bonnet Hamiltonian

We derive the gravitational Hamiltonian starting from the Gauss-Bonnet action, keeping track of all surface terms. This is done using the language of orthonormal frames and forms to keep things as tidy as possible. The surface terms in the Hamiltonian give a remarkably simple expression for the total energy of a spacetime. This expression is consistent with energy expressions found in hep-th/02...

Hamiltonian stability and subanalytic geometry

In the 70’s, Nekhorochev proved that for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time with respect to the size of the perturbation, provided that the unperturbed Hamiltonian satisfies some generic transversality condition known as steepness. Using theorems of real subanalytic geometry...

Stability of Structured Hamiltonian Eigensolvers

Hamiltonian flows, cotangent lifts, and momentum maps

Let (M,ω) and (N, η) be symplectic manifolds. A symplectomorphism F : M → N is a diffeomorphism such that ω = F ∗η. Recall that for x ∈ M and v1, v2 ∈ TxM , (F η)x(v1, v2) = ηF (x)((TxF )v1, (TxF )v2); TxF : TxM → TF (x)N . (A tangent vector at x ∈ M is pushed forward to a tangent vector at F (x) ∈ N , while a differential 2-form on N is pulled back to a differential 2-form on M .) In these not...

Geometric-Arithmetic Index of Hamiltonian Fullerenes

A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.