The paper describes an algorithm which generates those Hamiltonian circuits of a given cubic planar map which include some chosen edge of the map. A simple extension of the method results in the generation of all the Hamiltonian circuits of the map. The algorithm can readily be implemented on a digital computer, subject to limitations on storage. A general property of the generating function de...

Hamiltonian system LetA ⊆ R be an open set andH :A×R×R → R be a smooth function (A×R is called the phase space). Consider the system of ordinary differential equations q̇k = ∂H(q, p, t)/∂pk, ṗk = −∂H(q, p, t)/∂qk, for k = 1, . . . , d. The equations are called Hamilton equations, and H is called a Hamiltonian function. A dynamical system described by Hamilton equations is called a Hamiltonian sy...

A contactomorphism is a diffeomorphism ψ : M → M which preserves the contact structure ξ. This means that ψα = eα for some smooth function h : M → . A contact isotopy is a smooth family of contactomorphisms ψs : M → M such that ψ sα = e sα for all s. Any such isotopy with ψ0 = id and h0 = 0 is generated by Hamiltonian functions Hs : M → as follows. Each Hamiltonian function Hs determines a Hami...

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann z...

A semiclassical approximation for an evolving density operator, driven by a “closed” hamiltonian operator and “open” markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the hamiltonian operator is a quadratic function and the Lindblad operators ...

We investigate here how far we can extend the notion of a Halin graph such that hamiltonicity is preserved. Let H = T ∪ C be a Halin graph, T being a tree and C the outer cycle. A k-Halin graph G can be obtained from H by adding edges while keeping planarity, joining vertices of H − C, such that G − C has at most k cycles. We prove that, in the class of cubic 3-connected graphs, all 14-Halin gr...