In this paper we study a general near-Hamiltonian polynomial system on the plane. We suppose the unperturbed system has a family of periodic orbits surrounding a center point and obtain some sufficient conditions to find the cyclicity of the perturbed system at the center or a periodic orbit. In particular, we prove that for almost all polynomial Hamiltonian systems the perturbed systems with p...

In this paper we study isochronicity and linearizability of planar polynomial Hamiltonian systems. First we prove a theorem which supports a negative answer to the following open question: Do there exist planar polynomial Hamiltonian systems of even degree having an isochronous center? stated by Jarque and Villadelprat in the J. Differential Equations 180 (2002), 334–373. Additionally we obtain...

. . . . . . . . Introduction . . . . . . . . Hamiltonian Guiding Center Theory Numerical Integration . . . . Interpretation of Results . . . . Acknowledgements . . . . . . References . . . . . . . . . Figures . . . . . . . . . . ii . . . . . . . . . .1 . . . . . . . . . .1 . . . . . . . . . .1 . . . . . . . . . . 2 . . . . . . . . . . 3 . . . . . . . . . . 3 . . . . . . . . . . 3 . . . . . . . ...

the paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. attention goes to the number of limit cycles produced by the period annulus under perturbations. by using the appropriate p...

The adiabatic motion of a charged, spinning, quantum particle in a two dimensional magnetic field is studied. A suitable set of operators generalizing the cinematical momenta and the guiding center operators of a particle moving in a homogeneous magnetic field is constructed. This allows us to separate the two degrees of freedom of the system into a fast and a slow one, in the classical limit, ...

In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors obtained by tight binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave f...

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...