Homoclinic orbits for a class of discrete periodic Hamiltonian systems

Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

Homoclinic orbits for discrete Hamiltonian systems with subquadratic potential

where n ∈ Z, u ∈ RN , u(n) = u(n + ) – u(n) is the forward difference operator, p,L : Z→ RN×N and W : Z× RN → R. As usual, we say that a solution u(n) of system (.) is homoclinic (to ) if u(n)→  as n→±∞. In addition, if u(n) ≡ , then u(n) is called a nontrivial homoclinic solution. In general, system (.) may be regarded as a discrete analogue of the following second order Hamiltonian sy...

MULTIPLE PERIODIC SOLUTIONS FOR A CLASS OF NON-AUTONOMOUS AND CONVEX HAMILTONIAN SYSTEMS

In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.  

Periodic Orbits of Hamiltonian Systems

5 The Variational principles and periodic orbits 21 5.1 Lagrangian view point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2 Hamiltonian view point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.3 Fixed energy problem, the Hill’s region . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.4 Continuation of periodic orbits as critical p...

Singular Perturbation Theory for Homoclinic Orbits in a Class of Near-Integrable Hamiltonian Systems∗

This paper describes a new type of orbits homoclinic to resonance bands in a class of near-integrable Hamiltonian systems. It presents a constructive method for establishing whether small conservative perturbations of a family of heteroclinic orbits that connect pairs of points on a circle of equilibria will yield transverse homoclinic connections between periodic orbits in the resonance band r...