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 estab...

The distinguishing characteristic of the elliptic restricted three-body problem is a time-varying potential field resulting in non-autonomous and non-integrable dynamics. The purpose of this study is to normalize the system dynamics about the circular case and about one of the triangular Lagrange points by applying a method of canonical perturbation theory introduced by Hori and Deprit in the 1...

We give a precise statement for KAM theorem in a neighbourhood of an elliptic equilib rium point of a Hamiltonian system If the frequencies of the elliptic point are nonresonant up to a certain order K and a nondegeneracy condition is ful lled we get an estimate for the measure of the complement of the KAM tori in a neighbourhood of given radius Moreover if the frequencies satisfy a Diophantine...

In this paper the asymptotic expansion of first-order Melnikov function of a heteroclinic loop connecting a cusp and a nilpotent saddle both of order one for a planar near-Hamiltonian system are given. Next, we consider the bifurcation of limit cycles of a class of hyper-elliptic Liénard system with this kind of heteroclinic loop. It is shown that this system can undergo Poincarè bifurcation fr...

A binary system composed of an oscillating and rotating coplanar dusty disk and a point mass is considered. The conservative dynamics is treated on the Newtonian level. The effects of gravitational radiation reaction and wave emission are studied to leading quadrupole order. The related waveforms are given. The dynamical evolution of the system is determined semi-analytically exploiting the Ham...

in this paper mathematical structure of time-dependent lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent lagrangian systems are considered. starting point is time-independent lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to the...