The equations of classical spin-orbit motion can be extended to a Hamiltonian system in 9-dimensional phase space by introducing a coupled spin-orbit Poisson bracket (18) and a Hamiltonian function (20). After this extension and by establishing connections between initial and extended systems it becomes possible to apply the methods of the theory of Hamiltonian systems to the study of polarized...

We present two 2-body Hamiltonians that approximate the exact PH-Pfaffian wavefunction with their ground states for all system sizes where this has been numerically constructed to date. The wavefunctions have high overlap original and reproduce well low-lying entanglement spectrum structure factor. generating are obtained by an optimisation procedure three four pseudopotentials varied in neighb...

When a Hamiltonian system has a \Kinetic + Potential" structure, the resulting ow is locally a geodesic ow. But there may be singularities of the geodesic structure, so the local structure does not always imply that the ow is globally a geodesic ow. In order for a ow to be a geodesic ow, the underlying manifold must have the structure of a unit tangent bundle. We develop homological conditions ...

Given the Hamiltonian nature and conservation laws of the Korteweg-de Vries equation, the simulation of the solitary waves of this equation by numerical methods should be effected in such a way as to maintain the Hamiltonian nature of the problem. A semidiscrete finite element approximation of Petrov-Galerkin type, proposed by R. Winther, is analyzed here. It is shown that this approximation is...

It is now well known that symplectic integrators lose many of their desirable properties when variable step sizes are used. The most common approach to combine adaptive step sizes and symplectic integrators involves the Poincaré transformation of the original Hamiltonian. In this article, we provide a framework for the construction of variational integrators using the Poincaré transformation. S...

Hamiltonian stationary Lagrangian surfaces are Lagrangian surfaces of a given four-dimensional manifold endowed with a symplectic and a Riemannian structure, which are critical points of the area functional with respect to a particular class of infinitesimal variations preserving the Lagrangian constraint: the compactly supported Hamiltonian vector fields. The Euler–Lagrange equations of this v...

Let (M,ω) be a closed symplectic manifold. Given a function H : M → R the Hamiltonian vector field XH determined by the Hamiltonian H is defined by the formula XH ω = −dH. Then LXHω = 0, and hence the flow generated by XH preserves the symplectic form ω. If one has a family of functions Ht : M → R, t ∈ [0, 1], one gets a family of Hamiltonian vector fields XHt which generate an isotopy ft : M →...

In this paper several possibilities are considered for constructing test functions which reveal generic one parameter bifurcations of equilibria of Hamiltonian systems. These are alternatives to computing all the eigenvalues of the linearized system. Because of the Hamiltonian structure, most test functions that are used for general systems do not work here. Typically a test function that shoul...