Aperiodic Order is concerned with the investigation of discrete structures in space, such as point sets or tilings, which possess a certain degree of order while not showing any translational symmetry. A mathematical introduction to the field is provided by the book Aperiodic Order, recently published by Cambridge University Press.
Dynamical systems (often loosely referred to as "chaos theory") is the study of the solutions of nonlinear differential equations (or of maps in the case of discrete-time systems). Research in applied nonlinear dynamical systems includes the study of the transition to chaos, which often has remarkable properties that are "universal", i.e. common to a large class of models.