Dynamics
Dynamics at Glasgow focuses on topological dynamics and Teichmüller dynamics. Topological dynamics is the general study of the long term behaviour of group actions on topological spaces focusing on themes such as recurrence conditions, periodic orbits, entropy, chaos and stability. Typically, the dynamics is studied through topological and geometric invariants that reduce the complexity of the system to computable invariants that reflect specified aspects of the system. The wide variety of dynamics that fit into this framework makes topological dynamics a fruitful area of modern research. Specific dynamical systems that are studied in Glasgow include symbolic dynamics, self-similar group actions, tiling dynamical systems, Smale spaces and Cantor minimal dynamics. Teichmüller dynamics is the study of the dynamics of the moduli space of Riemann surfaces. The ubiquity of Riemann surfaces in mathematics connects Teichmüller dynamics with other fields such as rational maps, hyperbolic 3-manifolds and rational billiards.