# Galerkinï¿½s method, monotonicity and linking for indefinite Hamiltonian systems with bounded potential energy

## Related Articles

- Slow-fast hamiltonian dynamics near a ghost separatix loop. Lerman, L.; Gelfreich, V. // Journal of Mathematical Sciences;Apr2005, Vol. 126 Issue 5, p1445
We study the behavior of a slow-fast (singularly perturbed) Hamiltonian system with two degrees of freedom, losing one degree of freedom at the singular limit?= 0, near its ghost separatrix loop, i.e., a homoclinic orbit to a saddle equilibrium of the slow (one degree of freedom) system. We show...

- Count of eigenvalues in the generalized eigenvalue problem. Chugunova, Marina; Pelinovsky, Dmitry // Journal of Mathematical Physics;May2010, Vol. 51 Issue 5, p052901
We study isolated and embedded eigenvalues in the generalized eigenvalue problem defined by two self-adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues. The generalized eigenvalue problem determines the spectral stability of nonlinear waves in...

- Logarithmic correction to the probability of capture for dissipatively perturbed Hamiltonian... Haberman, Richard; Ho, Eric K. // Chaos;Jun95, Vol. 5 Issue 2, p374
Analyzes Hamiltonian systems with a double homoclinic orbit connecting a saddle to itself. Existence of competing centers; Small dissipative perturbation causing the stable and unstable manifolds of the saddle point to break; Boundaries of the basins known to be tightly wound and spiral-like;...

- Variational Formulation for the Multisymplectic Hamiltonian Systems. Jing-Bo Chen // Letters in Mathematical Physics;Mar2005, Vol. 71 Issue 3, p243
A variational formulation for the multisymplectic Hamiltonian systems is presented in this Letter. Using this variational formulation, we obtain multisymplectic integrators from a variational perspective. Numerical experiments are also reported.

- Conservation properties of numerical integrators for highly oscillatory Hamiltonian systems. Cohen, David // IMA Journal of Numerical Analysis;Jan2006, Vol. 26 Issue 1, p34
Modulated Fourier expansion is used to show long-time near-conservation of the total and oscillatory energies of numerical methods for Hamiltonian systems with highly oscillatory solutions. The numerical methods considered are an extension of the trigonometric methods. A brief discussion of...

- Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit. Maki, Atsuo; Umeda, Naoya; Ueta, Tetsushi // Journal of Marine Science & Technology;Mar2010, Vol. 15 Issue 1, p102
The chaos that appears in the ship roll equation in beam seas known as the escape equation has been intensively investigated because it is closely related to capsizing incidents. In particular, many applications of the Melnikov integral formula have been reported in the literature; however, in...

- Drift resonance of relativistic electrons with ULF waves as a nonlinear resonance. Gubar’, Yu. // Cosmic Research;Aug2010, Vol. 48 Issue 4, p300
The drift resonance of relativistic equatorial electrons with ultra low-frequency (ULF) waves in the dipole magnetic field is considered as a nonlinear resonance in a Hamiltonian system. There are no waves in the undisturbed system. An expression for the undisturbed Hamiltonian as a function of...

- Finite Hamiltonian systems: Linear transformations and aberrations. Wolf, K. B. // Physics of Atomic Nuclei;Mar2010, Vol. 73 Issue 3, p546
Finite Hamiltonian systems contain operators of position, momentum, and energy, having a finite number N of equally-spaced eigenvalues. Such systems are under the Ã¦is of the algebra su(2), and their phase space is a sphere. Rigid motions of this phase space form the group SU(2); overall...

- On Hamiltonian Systems with a Homoclinic Orbit to a Saddle-Center. Koltsova, O. // Journal of Mathematical Sciences;Jul2005, Vol. 128 Issue 2, p2787
We consider a real analytic Hamiltonian system with two degrees of freedom having a homoclinic orbit to a saddle-center equilibrium (two nonzero real and two nonzero imaginary eigenvalues). We take a two-parameter unfolding for such a system and show that in the nonresonance case, there are...