Hamiltonian Vector Research Articles

Sasaki–Ricci flow on Sasaki–Einstein space T1,1 and deformations

We study the transverse Kähler structure of the Sasaki–Einstein space [Formula: see text]. A set of local holomorphic coordinates is introduced and a Sasakian analogue of the Kähler potential is given. We investigate deformations of the Sasaki–Einstein structure preserving the Reeb vector field, but modifying the contact form. For this kind of deformations, we consider the Sasaki–Ricci flow which converges in a suitable sense to a Sasaki–Ricci soliton. Finally, it is described the constructions of Hamiltonian holomorphic vector fields and Hamiltonian function on the [Formula: see text] manifold.

Generalized Kähler–Einstein Metrics and Energy Functionals

Abstract.In this paper, we consider a generalized Kähler–Einstein equation on a Kähler manifold M. Using the twisted 𝒦–energy introduced by Song and Tian, we show that the existence of generalized Kähler–Einstein metrics with semi–positive twisting (1, 1)–form θ is also closely related to the properness of the twisted 𝒦-energy functional. Under the condition that the twisting form θ is strictly positive at a point or M admits no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of generalized Kähler–Einstein metric implies a Moser–Trudinger type inequality.

On the Hamiltonian Flow of Brake Hamiltonian System

This paper studies the Hamiltonian flow of the brake Hamiltonian dynamical system on the symmetrical symplectic manifold. By using the transformation law of Hamiltonian diffeomorphisms and the Hamiltonian vectors, this paper describes the characteristics of the Hamiltonian flows and proves that the Hamiltonian flows are invariant under some transformations.

Oscillatory pattern formation in a neural dynamical system governed by a mutual Hamiltonian and gradient vector field structure

Oscillatory pattern formation in a neural dynamical system governed by a mutual Hamiltonian and gradient vector field structure

Limit Cycles Close to Infinity of Certain Non-Linear Differential Equations

AbstractThrough successive radial perturbations of a certain planar Hamiltonian polynomial vector field of degree 2K + 1, we obtain a least K limit cycles containing (2K + 1)2 singularities.

On the canonical variational 2-form and the canonical transformation of fields

Let field variables xi (x)=(q,p) be a set of coordinates on the infinity 2n-dimensional cotangent bundle T*M and VF, VG the Hamiltonian flow vectors of T*M. The canonical variational 2-form omega u2( xi ) is defined by omega 2( xi )(VF,VG)= integral dnx( delta G/ delta qi)( delta F/ delta pi)-( delta G/ delta pi)( delta F/ delta qi) and obtained as omega 2( xi )= integral dnx delta pi/ delta qi. The condition of the field canonical transformation g: xi to eta becomes omega 2( xi = omega 2( eta ). The general theory of canonical transformations of fields is established. In particular, some examples of solving field equations and of field quantisation are given.

Cohomology of Hamiltonian and related formal vector field lie algebras

Cohomology of Hamiltonian and related formal vector field lie algebras

Cohomology of the Lie algebra of Hamiltonian formal vector fields

Cohomology of the Lie algebra of Hamiltonian formal vector fields

On determining the secular and critical effects in the motion of satellites by means of a nonsingular set of vectorial elements

Under the influence of the sun and the moon a highly eccentric orbit of a satellite can become a nearly circular one or a nearly circular orbit might become eccentric. In light of this I suggest a combination of the Gibbsian rotation vector and the Hamiltonian vector as a nonsingular set of elements to be used for all eccentricities and all inclinations. The method of Halphen is suggested for the computation of secular effects, and the method of Liouville for the computation of the near resonance effects caused by the commensurability of mean motions of the disturbed and the disturbing body. The combination of these two methods can give information about the general behavior of the orbit of a minor planet over an interval of some thousands of years, and of an artificial satellite moving in cislunar space over an interval of a number of years.

Vectors, &c., at the British Association

IN the report (August 30) of the discussion on the use and notation of vector analysis at the British Association is stated that I “deplored the substitution of vectors for quaternions.” The statement is misleading, for was it not Hamilton more than any other single man who taught us how to use vectors in product and quotient combinations? What I did and do deplore is the substitution of non-quaternionic vector algebras in all their variety of notation for the Hamiltonian or quaternionic vector algebra—a very different thing.