Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
Laser beam machiningLaser beam machining (LBM) is a form of machining that uses heat directed from a laser beam. This process uses thermal energy to remove material from metallic or nonmetallic surfaces. The high frequency of monochromatic light will fall on the surface, thus heating, melting and vaporizing the material due to the impinge of photons (see Coulomb explosion). Laser beam machining is best suited for brittle materials with low conductivity, but can be used on most materials. Laser beam machining can be done on glass without melting the surface.
Poincaré mapIn mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system. More precisely, one considers a periodic orbit with initial conditions within a section of the space, which leaves that section afterwards, and observes the point at which this orbit first returns to the section.
