In this paper we introduce a general methodology for computing numerically the normal form around a periodic orbit of an autonomous analytic Hamiltonian system The process follows two steps First we expand the Hamiltonian in suit able coordinates around the orbit and second we perform a standard normal form scheme based on the Lie series method This scheme is carried out up to some nite order a...

In this paper we introduce a general methodology for computing (numerically) the normal form around a periodic orbit of an autonomous analytic Hamiltonian system. The process follows two steps. First, we expand the Hamiltonian in suitable coordinates around the orbit and second, we perform a standard normal form scheme, based on the Lie series method. This scheme is carried out up to some nite ...

This paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎With the help of the Nehari manifold and Palais-Smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a c...

We present a new approach to proving the existence of semi-classical bound states of the non-linear Schrödinger equation which are concentrated near a finite set of non-degenerate critical points of the potential function. The method is based on considering a system of non-linear elliptic equations. The positivity of the solutions is considered. It is shown how the same method yields “multi-bum...

The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the Poincaré disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard-Fu...

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by parti...

We provide a condition for f -ergodicity of strong Markov processes at a subgeometric rate. This condition is couched in terms of a supermartingale property for a functional of the Markov process. Equivalent formulations in terms of a drift inequality on the extended generator and on the resolvent kernel are given. Results related to (f, r)-regularity and to moderate deviation principle for int...

In this paper we describe the geometry of the energy momentum mapping of the complexified spherical pendulum. For background on the classical spherical pendulum we refer the reader to [4, chpt. IV]. We show that this complex Hamiltonian system is Mumford-Jacobi completely integrable [9, p.3.51–3.53] and admits an analogue of the period lattice [5] and action angle coordinates [4, Apend. D]. Fol...

General reduction of the elliptic hypergeometric equation to level complex functions is described. The derived generalized Hamiltonian eigenvalue problem for new rational integrable $N$-body systems emerging from particular degenerations Ruijsenaars and van Diejen models.

We identify a new symmetry for the equations governing odderon amplitudes, corresponding in the Regge limit of QCD to the exchange of 3 reggeized gluons. The symmetry is a modular invariance with respect to the unique normal subgroup of SL(2, Z) of index 2. This leads to a natural description of the Hamiltonian and conservation-law operators as acting on the moduli space of elliptic curves with...