Mather Theory

Mather Theory, developed by John Mather, is a mathematical framework in the field of dynamical systems that studies the long-term behavior of particles or objects moving under smooth, deterministic forces. It focuses on identifying special collections of states, called invariant sets, where the system's trajectories often settle or structure themselves. These sets can explain the patterns and stability within complex motions, such as planetary orbits or other natural phenomena. Mather Theory helps mathematicians understand how minimal energy configurations shape the global behavior of dynamical systems, offering insights into stability, chaos, and optimal paths.