<p style='text-indent:20px;'>In the framework of nonlinear stability elliptic equilibria in Hamiltonian systems with <inline-formula><tex-math id="M3">\begin{document}$ n $\end{document}</tex-math></inline-formula> degrees freedom we provide a criterion to obtain type formal stability, called Lie stability. Our result generalises previous approaches, as exponential...

We propose a closed-form (i.e. without expansion in the orbital eccentricities) scheme for computations perturbation theory restricted three-body problem (R3BP) when massless particle is an orbit exterior to one of primary perturber. Starting with multipole barycentric (Jacobi-reduced) Hamiltonian, we carry out sequence normalizations Delaunay variables by Lie series, leading secular Hamiltonia...

We prove the existence of infinitely many periodic solutions accumulating to zero for the one–dimensional nonlinear wave equation (vibrating string equation). The periods accumulate to zero and are both rational and irrational multiples of the string length. 1. A Poincaré conjecture. The wave equation is an infinite dimensional hamiltonian system. The importance of periodic solutions for finite...

Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first reviewed, and then adaptive multilevel finite element methods for approximating solutions to this class of problems are considered in some detail. Two a posterio...

We consider the planar double pendulum where its center of mass is attached in an elliptic orbit. We case rods have variable length, varying according to radius vector make Hamiltonian view problem, find four linearly stable equilibrium positions and construct boundary curves stability/instability regions space parameters associated with length eccentricity

In this note we present molecular dynamics integration schemes that combine optimized splitting and gradient methods with exact free rotational motion for rigid body systems and discuss their relative merits. The algorithms analyzed here are based on symplectic, timereversible schemes that conserve all relevant constants of the motion. It is demonstrated that although the algorithms differ in t...

Many equations can be expressed as a cubic nonlinear Schrödinger (NLS) equation with additional terms, such as the Davey-Stewartson (DS) system [1]. As it is the case for the NLS equation, the solutions of the DS system are invariant under the pseudo-conformal transformation. For the elliptic NLS, this invariance plays a key role in understanding the blow-up profile of solutions, whereas in the...