We obtain an algebraic interpretation by means of the Picard-Vessiot theory of a result by Ziglin about the self-intersection of complex separatrices of time-periodically perturbed one-degree of freedom complex analytical Hamiltonian systems.
Se discuten algunos aspectos del problema de Landau-Hall hiperbólico. El álgebra de Lie de las simetrías infinitesimales de este problema se da explícitamente, resultando ser isomorfa a so(2,1) y que sus invariantes Noether asociados son los momentos angulares hiperbólicos. Asimismo se desarrolla la formulación hamiltoniana, lo que nos permitirá obtener la variedad de órbitas de energía constante de este problema mediante técnicas de reducción simpléctica.
Let be the Lie group of all Euclidean motions in the Euclidean space , let be its Lie algebra and the space dual to . This paper deals with structures of the subspaces of which are formed by all the forces whose power exerted on the robot effector is zero.
The external derivative on differential manifolds inspires graded operators on complexes of spaces , , stated by dual to a Lie algebra . Cohomological properties of these operators are studied in the case of the Lie algebra of the Lie group of Euclidean motions.
In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation...