Undoubtedly one of the most exciting frontiers in physics today is the study of nonlinear systems, more popularly called chaos. Chaos is the key to many time-dependent processes in as varied fields as meteorology (such as weather modeling), mechanics (the three-body problem in gravitational fields), and economics (prediction of trends in the stock market).
Margis, Richard, "Nonlinear Dynamics and the Lorenz Water Wheel" (1991). Opportunities for Undergraduate Research Experience Program (OURE). 141.