Several years ago, I was intensively studying semilinear biharmonic elliptic equations, a
topic quite far away from suspension bridges. In 2009, I was invited at a conference in …

Quasihalo orbits are Lissajous trajectories librating about the well known halo orbits. The
main feature of these orbits is that they keep an exclusion zone in the same way that halo …

We model the roadway of a suspension bridge as a thin rectangular plate and we study in
detail its oscillating modes. The plate is assumed to be hinged on its short edges and free on …

A simple example is considered of Hill's equation ̈ x+(a^ 2+ bp (t)) x= 0, where the forcing
term p, instead of periodic, is quasi-periodic with two frequencies. A geometric exploration is …

We analyze the modulation instability induced by periodic variations of group velocity
dispersion and nonlinearity in optical fibers, which may be interpreted as an analogue of the …

Kolmogorov–Arnold–Moser (or KAM) Theory was developed for conservative (Hamiltonian)
dynamical systems that are nearly integrable. Integrable systems in their phase space …

Parametrically excited linear systems with oscillatory coefficients have been generally
modeled by Mathieu or Hill equations (periodic coefficients) because their stability and …

We consider the Kuramoto model of coupled oscillators with nearest-neighbour coupling
and additive white noise. We show that synchronous solutions which are stable without the …

We consider the nonlinear nonlocal beam evolution equation introduced by Woinowsky–
Krieger [38]. We study the existence and behavior of periodic solutions: these are called …

The Ne ı˘ mark–Sacker bifurcation, or Hopf bifurcation for maps, is a well-known bifurcation
for smooth dynamical systems. At this bifurcation a periodic orbit loses stability, and, except …