Quasi-periodic solutions of Hamiltonian systems

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 Solutions of Second Order Hamiltonian Systems

We provide sufficient conditions for the existence of periodic solutions of the second order Hamiltonian system −x′′ − λx = εV ′ x (t, x) , where ε is a small parameter, x ∈ R and V (t, x) is 2π-periodic in t. Moreover we provide two applications.

Periodic solutions of even Hamiltonian systems onthe

We consider the Hamiltonian system (HS) ?J _ z = H z (t; z) where H 2 C 2 (R R 2N ; R) is 2-periodic in all variables, so (HS) induces a Hamiltonian system on the torus T 2N. In addition we assume that H is even in the z-variable. This implies the existence of 2 2N trivial stationary solutions of (HS). We are interested in the existence of nontrivial periodic solutions. Observe that the Arnol'd...

Periodic Solutions of Spatially Periodic, Even Hamiltonian Systems

Degenerate Bifurcation Points of Periodic Solutions of Autonomous Hamiltonian Systems

We study connected branches of non-constant 2π-periodic solutions of the Hamilton equation ẋ(t) = λJ∇H(x(t)), where λ ∈ (0,+∞), H ∈ C(R ×Rn,R) and ∇H(x0) = [ A 0 0 B ] for x0 ∈ ∇H−1(0). The Hessian ∇H(x0) can be singular. We formulate sufficient conditions for the existence of such branches bifurcating from given (x0, λ0). As a consequence we prove theorems concerning the existence of connected...