in this paper, the maximal dissipative extensions of a symmetric singular 1d discrete hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the hilbert space ℓ_{ω}²(z;c²) (z:={0,±1,±2,...}) are considered. we consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. for each of these cases we establish a self...

Abstract We argue that Hamiltonian mechanics is more fundamental than Lagrangian mechanics. Our argument provides a non-metaphysical strategy for privileging one formulation of theory over another: ceteris paribus , general fundamental. illustrate this criterion through novel interpretation classical mechanics, based on three physical conditions. Two these conditions suffice recovering A third ...

Quantum chaos entails the investigation of the quantization of classical Hamiltonian systems with chaotic dynamics. It is particularly interesting to consider the quantization of systems with mixed regular integrable and chaotic dynamics, as typical classical Hamiltonian systems possess mixed dynamics, with islands of integrability situated in a chaotic sea. One particularly appealing example c...

In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines. We prove if central subsystem, i.e. defined between lines, has real center and other subsystems have centers or saddles, then at least appear after perturbations annulus. ...

Slowly varying conservative one-degree of freedom Hamiltonian systems are analyzed in the case of a saddle-center bifurcation. Away from unperturbed homoclinic orbits, strongly nonlinear oscillations are obtained using the method of averaging. A long sequence of nearly homoclinic orbits is matched to the strongly nonlinear oscillations before and after the slow passage. Usually solutions pass t...