Abstract: I'll consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. I'll first consider a free field theory on a torus with a time-dependent mass term. I'll further consider the gravity dual of a conformal field theory on a sphere in three spacetime dimensions, deformed by a doubletrace operator. The gravity dual of the theory with a constant unbounded potential develops big crunch singularities. Such singularities can be cured by dynamical stabilization: for sufficiently high frequencies the theory is dynamically stabilized and big crunches get screened by black hole horizons. I'll further discuss the response of AdS black branes to external time-dependent periodic boundary conditions (dual in the CFT to time-dependent deformations).
