A systematic research on the structure-preserving controller is investigated in this paper, including its applications to the secondorder, first-order, time-periodic, or degenerated astrodynamics, respectively. The general form of the controller is deduced for the typical Hamiltonian system in full feedback and position-only feedback modes, which is successful in changing the hyperbolic equilib...

We consider a singularly perturbed Hamiltonian system, which loses one degree of freedom at " = 0. Assume the slow manifold to be normally elliptic. In the case of an analytic Hamilton function it is shown that the slow manifold persists up to an exponentially small error term.

A Hamiltonian formulation of nonlinear, parallel propagating, travelling whistler waves is developed. The complete system of equations reduces to two coupled differential equations for the transverse electron speed u and a phase variable φ=φp − φe representing the difference in the phases of the transverse complex velocities of the protons and the electrons. Two integrals of the equations are o...

In this paper we look for existence results for nontrivial solutions to the system, ⎧ ⎪⎪⎨ ⎪⎪⎩ − u = v p |x |α in , − v = u q |x |β in , with Dirichlet boundary conditions, u = v = 0 on ∂ and α, β < N . We find the existence of a critical hyperbola in the (p, q) plane (depending on α, β and N ) below which there exists nontrivial solutions. For the proof we use a variational argument (a linking ...

We give an extension of the celebrated Birkhoff–Lewis theorem to the nonlinear wave equation. Accordingly we find infinitely many periodic orbits with longer and longer minimal periods accumulating at the origin, which is an elliptic equilibrium of the associated infinite dimensional Hamiltonian system.

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

Directional Quasi–Convexity (DQC) is a sufficient condition for Nekhoroshev stability, that is, stability for finite but very long times, of elliptic equilibria of Hamiltonian systems. The numerical detection of DQC is elementary for system with three degrees of freedom. In this article, we propose a recursive algorithm to test DQC in any number n ≥ 4 of degrees of freedom.