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.  

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian are elegant compact formalism classical mechanics, where the dynamics is fully determined by one scalar function, Hamiltonian. The solution trajectories often constrained to evolve on a submanifold linear vector space. In this work, we propose new approaches for acc...

We discuss QCD in the Hamiltonian frame work. We treat finite density QCD in the strong coupling regime. We present a parton-model inspired regularisation scheme to treat the spectrum (θ-angles) and distribution functions in QED 1+1. We suggest a Monte Carlo method to construct low-dimensionasl effective Hamiltonians. Finally, we discuss improvement in Hamiltonian QCD. 1. Introduction There are...

This paper intends to explore bifurcation behavior of limit cycles for a cubic Hamiltonian system with quintic perturbed terms using both qualitative analysis and numerical exploration. To obtain the maximum number of limit cycles, a quintic perturbed function with the form of R(x, y, λ) = S(x, y, λ) = mx2 + ny2 + ky4 − λ is added to a cubic Hamiltonian system, where m, n, k and λ are all varia...

We develop models of globular clusters (GCs) with a different approach by applying thermodynamic principles to a Boltzmann distribution function, with an Hamiltonian function which contains an effective potential depending on the kinetic energy of the stars, due to the effect of tidal interactions induced by the hosting galaxy. The Hamiltonian function is solution of the Fokker-Planck equation ...

We construct a proper C-smooth function on R such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.

For linear Hamiltonian systems, the reconstruction of the Poisson bracket from a given energy function and an Hamiltonian flow leads to simple quantization rules. They can also be used in the infinite dimensional case. From this point of view, we consider the examples of oscillators, free electro-magnetic fields and vibrating strings.

We consider the problem of quantum ‘‘reflection above the barrier,’’ introducing a distorted-wave Born approximation based on the primitive semiclassical Wentzel-Kramers-Brillouin wave function. The idea generalizes to the concept of an unperturbed Hamiltonian defined as the exact Hamiltonian plus small parts which ‘‘turn off’’ nonclassical processes such as barrier reflection and barrier tunne...