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 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 Picard...

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

We consider C Hamiltonian functions on compact 4-dimensional symplectic manifolds to study elliptic dynamics of the Hamiltonian flow, namely the so-called Newhouse dichotomy. We show that for any open set U intersecting a far from Anosov regular energy surface, there is a nearby Hamiltonian having an elliptic closed orbit through U . Moreover, this implies that for far from Anosov regular energ...

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...

The existence of lower-dimensional resonant bifurcating tori of parabolic, hyperbolic and elliptic normal stability types is proved to be generic and persistent in a class of n degrees of freedom (DOF) integrable Hamiltonian systems with n 3. Parabolic resonance (PR) (respectively, hyperbolic or elliptic resonance) is created when a small Hamiltonian perturbation is added to an integrable Hamil...

We show that elliptic Calogero-Moser system and its Lax operator found by Krichever can be obtained by hamiltonian reduction from the integrable hamiltonian system on the cotangent bundle to the central extension of the algebra of slN (C) currents. ∗email: [email protected] [email protected]

We give a precise statement of KAM theorem for a Hamiltonian system in a neighborhood of an elliptic equilibrium point If the frequencies of the elliptic point satisfy a Diophantine condition with exponent and a nondegeneracy condition is ful lled we show that in a neighborhood of radius r the measure of the complement of the KAM tori is exponentially small in r This result is obtained by putti...