A Gray code is a Hamilton path H on the n-cube, Q n. By labeling each edge of Q n with the dimension that changes between its incident vertices, a Gray code can be thought of as a sequence H = t 1 ; t 2 ; : : : ; t N-1 (with N = 2 n and each t i satisfying 1 t i n). The sequence H deenes an (undirected) graph of transitions, G H , whose vertex set is f1; 2; : : : ; ng and whose edge set E(G H) ...

We consider the computability of entropy and information in classical Hamiltonian systems. We define the information part and total information capacity part of entropy in classical Hamiltonian systems using relative information under a computable discrete partition. Using a recursively enumerable nonrecursive set it is shown that even though the initial probability distribution, entropy, Hamil...

It is shown that the natural framework for the solutions of any Schrödinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to handle unbounded Schrödinger Hamiltonians whose spectrum has a continuous part are disclosed. Those difficulties are overcome by using an appropriate Rigged Hi...

The main purpose of the paper is to give discrete-time counterpart for some strong (robust) stability results concerning periodic linear Hamiltonian systems. In the continuoustime version, these results go back to Liapunov and Žukovskii; their deep generalizations are due to Kreı̆n, Gel’fand, and Jakubovič and obtaining the discrete version is not an easy task since not all results migratemutati...

Kahan’s method and a two-step generalisation of the discrete gradient are both linearly implicit methods that can preserve modified energy for Hamiltonian systems with cubic Hamiltonian. These here investigated compared. The schemes applied to Korteweg–de Vries equation Camassa–Holm equation, numerical results presented analysed.

We analyze the Hamiltonian of the compactified D = 11 supermembrane with non-trivial central charge in terms of the matrix model constructed in [1]. Our main result provides a rigorous proof that the quantum Hamiltonian of the supersymmetric model has compact resolvent and thus its spectrum consists of a discrete set of eigenvalues with finite multiplicity.

We define a class of arbitrary high order symmetric one-step methods that, when applied to Hamiltonian systems, are capable of precisely conserving the Hamiltonian function when this is a polynomial, whatever the initial condition and the stepsize h used. The key idea to devise such methods is the use of the so called discrete line integral, the discrete counterpart of the line integral in cons...

This is an introductory report concerning our recent research on Hamiltonian structures. We will discuss variational identities associated with continuous and discrete spectral problems, and their applications to Hamiltonian structures of soliton equations. Our illustrative examples are the AKNS hierarchy and the Volterra lattice hierarchy associated with semisimple Lie algebras, and two hierar...

The stability of motion of attitude maneuvers of a torque-free rigid gyrostat with a discrete damper is investigated. The equations of motion are presented and non-dimensionalized, then rewritten as a singularly perturbed, noncanonical, Hamiltonian system. Conditions for equilibrium motions and for their stability are developed. Bifurcation diagrams are used to illustrate the stable and unstabl...