Related papers: A Note on Homoclinic Orbits for Second Order Hamil…
Heteroclinic connections between two distinct hyperbolic periodic orbits in conservative systems are important in a wide range of applications. On the other hand, it is theoretically challenging to find large amplitude connections from…
This is the second of two companion papers dedicated to the investigation of vortex motion on non-orientable surfaces. The first paper of the pair is predominantly concerned with establishing the Hamiltonian approach to systems of point…
The equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clariffied and two examples are presented in details.
We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct…
We present here a new method which applies well ordered symbolic dynamics to find unstable periodic and non-periodic orbits in a chaotic system. The method is simple and efficient and has been successfully applied to a number of different…
We give a necessary and sufficient condition for strong stability of low dimensional Hamiltonian systems, in terms of the iterates of a closed orbit and the Conley-Zehnder index. Applications to Mathieu equation and stable harmonic…
We develop a geometric mechanism to prove the existence of orbits that drift along a prescribed sequence of cylinders, under some general conditions on the dynamics. This mechanism can be used to prove the existence of Arnold diffusion for…
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…
We obtain existence and uniqueness for odd second order oscillators in the space of odd functions without topological assumptions on the nonlinear part.
The present paper is a review of counterexamples to the ``Hamiltonian Seifert conjecture'' or, more generally, of examples of Hamiltonian systems having no periodic orbits on a compact energy level. We begin with the discussion of the…
We discuss several new bi-Hamiltonian integrable systems on the plane with integrals of motion of third, fourth and sixth order in momenta. The corresponding variables of separation, separated relations, compatible Poisson brackets and…
We study focussing discrete nonlinear Schr\"{o}dinger equations and present a new variational existence proof for homoclinic standing waves (bright solitons). Our approach relies on the constrained maximization of an energy functional and…
The main result asserts the existence of noncontractible periodic orbits for compactly supported time dependent Hamiltonian systems on the unit cotangent bundle of the torus or of a negatively curved manifold whenever the generating…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
In this paper we explore the general conditions in order that a 2-dimensional natural Hamiltonian system possess a second invariant which is a polynomial in the momenta and is therefore Liouville integrable. We examine the possibility that…
We discuss a general procedure for arriving at the Hamilton-Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and…
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
We study the dynamics of a pair of parametrically-driven coupled nonlinear mechanical resonators of the kind that is typically encountered in applications involving microelectromechanical and nanoelectromechanical systems (MEMS & NEMS). We…
It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of…