Parametric instability in periodically perturbed dynamos

Vector modulational instability induced by parametric resonance in periodically tapered highly birefringent optical fibers

Invariant Tori for Periodically Perturbed Oscillators

The response of an oscillator to a small amplitude periodic excitation is discussed. In particular, sufficient conditions are formulated for the perturbed oscillator to have an invariant torus in the phase cylinder. When such an invariant torus exists, some perturbed solutions are in the basin of attraction of this torus and are thus entrained to the dynamical behavior of the perturbed system o...

Stability for quasi-periodically perturbed Hill’s equations

We consider a perturbed Hill’s equation of the form φ̈ + (p0(t) + εp1(t))φ = 0, where p0 is real analytic and periodic, p1 is real analytic and quasi-periodic and ε ∈ R is “small”. Assuming Diophantine conditions on the frequencies of the decoupled system, i.e. the frequencies of the external potentials p0 and p1 and the proper frequency of the unperturbed (ε = 0) Hill’s equation, but without ma...

Chaos in Periodically Perturbed Monopole + Quadrupole Like Potentials

The motion of a particle that suffers the influence of simple inner (outer) periodic perturbations when it evolves around a center of attraction modeled by an inverse square law plus a quadrupole-like term is studied. The equations of motion are used to reduce the Melnikov method to the study of simple graphics.

Gamow Vectors in a Periodically Perturbed Quantum System

We analyze the behavior of the wave function ψ(x, t) for one dimensional time-dependent Hamiltonian H = −∂2 x ± 2δ(x)(1 +2r cosωt) where ψ(x, 0) is compactly supported. We show that ψ(x, t) has a Borel summable expansion containing finitely many terms of the form P∞ n=−∞ e i3/2 √ kAk,ne −λkt+nωit, where λk represents the associated resonance. This expression defines Gamow vectors and resonances...