Global attractor

Summary

The global attractor of a dissipative dynamical system on a metric space is a compact invariant set. It attracts every bounded set of initial data. It contains all the long-time dynamics: all equilibria, periodic orbits and bounded complete trajectories. Many dissipative PDEs have a global attractor of finite fractal dimension, although the phase space is infinite-dimensional. Examples are reaction–diffusion equations and the two-dimensional Navier–Stokes equations.