  We study the evolution of a driven harmonic oscillator with a time-dependent
frequency $\omega_t \propto |t|$. At time $t=0$ the Hamiltonian undergoes a
point of infinite spectral degeneracy. If the system is initialized in the
instantaneous vacuum in the distant past then the asymptotic future state is a
squeezed state whose parameters are explicitly determined. We show that the
squeezing is independent on the sweeping rate. This manifests the failure of
the adiabatic approximation at points where infinitely many eigenvalues
collide. We extend our analysis to the situation where the gap at $t=0$ remains
finite. We also discuss the natural geometry of the manifold of squeezed
states. We show that it is realized by the Poincar\'e disk model viewed as a
K\"ahler manifold.
