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On the multiplicity of periodic solutions of an Hamiltonian system

100%

Timouni M.

Demonstratio Mathematica

2002

tom Vol. 35, nr 4

899-913

In this note, we are interested in the existence of multiple periodic solutions of nonautonomous Hamiltonian systems with bounded gradient of the type: Jx+-H'(t,x)+e(t) =0.

Spectral characterization of hydrogen-like atoms confined by oscillating systems

80%

Iacob F.

Open Physics

2014

tom 12

nr 9

628-636

The spectral characterization of Coulomb systems confined by a homogeneous pseudo-Gaussian oscillator is investigated. This is done using the efficient computational method of generating functionals. Also, this method is used for the spectral characterization of homogeneous harmonic oscillator confinement, treated as a particular case of pseudo-Gaussian oscillator confinement. Finally, confinement by an impenetrable sphere of finite radius is considered by studying its conjugate effect along with a harmonic oscillator.

Buckling of cylindrical shells under external pressure in a Hamiltonian system

80%

Sun J. , Xu X. , Lim C. W.

Journal of Theoretical and Applied Mechanics

2014

tom Vol. 52 nr 3

641--653

In this article, the elastic buckling behavior of cylindrical shells under external pressure is studied by using a symplectic method. Based on Donnell’s shell theory, the governing equations which are expressed in stress function and radial displacement are re-arranged into the Hamiltonian canonical equations. The critical loads and buckling modes are reduced to solving for symplectic eigenvalues and eigenvectors. The buckling solutions are mainly grouped into four categories according to the natures of the buckling modes. The effects of geometrical parameters and boundary conditions on the buckling loads and modes are examined in detail.

C1 non-integrability of a hydrogen atom in a circularly polarized microwave field

80%

Guirao J. , López M. , Vera J.

Open Physics

2012

tom 10

nr 4

742-748

Barrabés et al. [Physica D, 241(4), 333–349, 2012] consider the problem of the hydrogen atom interacting with a circularly polarized microwave field modeled as a planar perturbed Kepler problem. For different values of the parameter, the authors offer some numerical evidence of the non-integrability of this problem. The objective of the present work is to give an analytical proof of the C1 non-integrability of this problem for any value of the parameter using the averaging theory as a main tool.

Closed orbits for a class of Hamiltonian systems

70%

Timouni M.

Demonstratio Mathematica

1998

tom Vol. 31, nr 1

1-10

In this paper we prove the

On existence of subharmonic orbits in perturbed Hamiltonian systems

60%

Yang X.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

tom Vol. 48, no 2

221-225

In this paper the existence of subharmonic orbits in planar Hamiltonian system x = f(x) + [epsilon]g(x,t) is revisited. The existing error in treatment on this problem is discussed and a new rigorous treatment is given.

Symplectic singularities and solvable Hamiltonian mappings

60%

Fukuda T. , Janeczko S.

Demonstratio Mathematica

2015

tom Vol. 48, nr 2

118--146

We study singularities of smooth mappings (…) of R2n into symplectic space (…) by their isotropic liftings to the corresponding symplectic tangent bundle (…). Using the notion of local solvability of lifting as a generalized Hamiltonian system, we introduce new symplectic invariants and explain their geometric meaning. We prove that a basic local algebra of singularity is a space of generating functions of solvable isotropic mappings over (…) endowed with a natural Poisson structure. The global properties of this Poisson algebra of the singularity among the space of all generating functions of isotropic liftings are investigated. The solvability criterion of generalized Hamiltonian systems is a strong method for various geometric and algebraic investigations in a symplectic space. We illustrate this by explicit classification of solvable systems in codimension one.

Combined algorithm for finding conservation laws and implectic operators for the Boussinesq-Burgers nonlinear dynamical system and its finite dimensional reductions

41%

Kindybaliuk A. , Prytula M.

Journal of Applied Mathematics and Computational Mechanics

2014

tom Vol. 13, nr 3

85--99

In the article the combined algorithm for finding conservation laws and implectic operators has been proposed. Using the Novikov-Bogoyavlensky method the finite dimensional reductions have been found. The structure of invariant submanifolds has been examined. Having analyzed phase portraits of Hamiltonian systems, partial periodical solutions have been found.