Electronic States in Perturbed Periodic Systems

Electronic States in Perturbed Periodic Systems

The occurrence in perturbed periodic systems, such as impure crystals, of localized states with discrete energies is discussed from both qualitative and quantitative points of view. Semiclassical considerations, modi6ed in the usual way by wave concepts, make it clear that impurities will give rise to impurity states above or below corresponding permitted bands of energy, according as the ionic...

Electronic states on a lattice in periodic magnetic fields

Periodic Orbits of Hamiltonian Systems: Applications to Perturbed Kepler Problems

We provide for a class of Hamiltonian systems in the action– angle variables sufficient conditions for showing the existence of periodic orbits. We expand this result to the study of the existence of periodic orbits of perturbed spatial Keplerian Hamiltonians with axial symmetry. Finally, we apply these general results for finding periodic orbits of the Matese– Whitman Hamiltonian, of the spati...

Poincaré Index and Periodic Solutions of Perturbed Autonomous Systems

Classical conditions for the bifurcation of periodic solutions in perturbed auto-oscillating and conservative systems go back to Malkin and Mel’nikov, respectively. These authors’ papers were based on the Lyapunov–Schmidt reduction and the implicit function theorem, which lead to the requirement that both the cycles and the zeros of the bifurcation functions be simple. In this paper a geometric...

Multiple Periodic Solutions for Perturbed Second-order Impulsive Hamiltonian Systems

The existence of three distinct periodic solutions for a class of perturbed impulsive Hamiltonian systems is established. The techniques used in the proofs are based on variational methods. AMS Subject Classification: 34B15